LMFDB - Embedded newform 819.2.fy.a.50.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(50,819)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("819.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fy (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.10
Character	$\chi$	$=$	819.50
Dual form			819.2.fy.a.344.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.603210 - 2.25121i) q^{2} +(0.907564 + 1.47524i) q^{3} +(-2.97204 + 1.71591i) q^{4} +(-1.06637 - 3.97976i) q^{5} +(2.77362 - 2.93300i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.35963 + 2.35963i) q^{8} +(-1.35266 + 2.67775i) q^{9} +O(q^{10})$	\(q+(-0.603210 - 2.25121i) q^{2} +(0.907564 + 1.47524i) q^{3} +(-2.97204 + 1.71591i) q^{4} +(-1.06637 - 3.97976i) q^{5} +(2.77362 - 2.93300i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.35963 + 2.35963i) q^{8} +(-1.35266 + 2.67775i) q^{9} +(-8.31604 + 4.80127i) q^{10} +(-5.49728 + 1.47299i) q^{11} +(-5.22869 - 2.82717i) q^{12} +(-0.976138 + 3.47090i) q^{13} +(-2.01838 - 1.16531i) q^{14} +(4.90329 - 5.18504i) q^{15} +(0.456865 - 0.791313i) q^{16} +(0.220817 - 0.382467i) q^{17} +(6.84411 + 1.42987i) q^{18} +(0.775062 - 0.207677i) q^{19} +(9.99821 + 9.99821i) q^{20} +(1.68490 + 0.401407i) q^{21} +(6.63203 + 11.4870i) q^{22} +1.27503 q^{23} +(-1.33950 + 5.62254i) q^{24} +(-10.3712 + 5.98782i) q^{25} +(8.40255 + 0.103809i) q^{26} +(-5.17793 + 0.434735i) q^{27} +(-0.888219 + 3.31488i) q^{28} +(-4.93302 - 2.84808i) q^{29} +(-14.6303 - 7.91068i) q^{30} +(8.22040 - 2.20265i) q^{31} +(4.38964 + 1.17620i) q^{32} +(-7.16215 - 6.77297i) q^{33} +(-0.994213 - 0.266399i) q^{34} +(-3.56816 - 2.06008i) q^{35} +(-0.574617 - 10.2794i) q^{36} +(-10.4305 - 2.79484i) q^{37} +(-0.935051 - 1.61956i) q^{38} +(-6.00631 + 1.71003i) q^{39} +(6.87453 - 11.9070i) q^{40} +(0.839742 - 0.839742i) q^{41} +(-0.112695 - 4.03519i) q^{42} +10.5095i q^{43} +(13.8106 - 13.8106i) q^{44} +(12.0992 + 2.52777i) q^{45} +(-0.769114 - 2.87037i) q^{46} +(-0.0352210 + 0.131446i) q^{47} +(1.58201 - 0.0441826i) q^{48} -1.00000i q^{49} +(19.7359 + 19.7359i) q^{50} +(0.764635 - 0.0213548i) q^{51} +(-3.05463 - 11.9906i) q^{52} -0.940462i q^{53} +(4.10206 + 11.3944i) q^{54} +(11.7243 + 20.3071i) q^{55} +3.33703 q^{56} +(1.00979 + 0.954921i) q^{57} +(-3.43599 + 12.8233i) q^{58} +(-1.70873 + 6.37705i) q^{59} +(-5.67573 + 23.8238i) q^{60} -1.23929 q^{61} +(-9.91726 - 17.1772i) q^{62} +(0.936980 + 2.84992i) q^{63} -12.4190i q^{64} +(14.8543 + 0.183517i) q^{65} +(-10.9271 + 20.2090i) q^{66} +(-3.59577 - 3.59577i) q^{67} +1.51561i q^{68} +(1.15717 + 1.88098i) q^{69} +(-2.48532 + 9.27533i) q^{70} +(0.243859 + 0.910095i) q^{71} +(-9.51028 + 3.12673i) q^{72} +(1.75591 - 1.75591i) q^{73} +25.1671i q^{74} +(-18.2460 - 9.86568i) q^{75} +(-1.94716 + 1.94716i) q^{76} +(-2.84560 + 4.92873i) q^{77} +(7.47271 + 12.4900i) q^{78} +(-0.384719 - 0.666354i) q^{79} +(-3.63643 - 0.974377i) q^{80} +(-5.34064 - 7.24414i) q^{81} +(-2.39698 - 1.38390i) q^{82} +(-15.6094 - 4.18253i) q^{83} +(-5.69635 + 1.69813i) q^{84} +(-1.75760 - 0.470948i) q^{85} +(23.6592 - 6.33946i) q^{86} +(-0.275433 - 9.86220i) q^{87} +(-16.4473 - 9.49585i) q^{88} +(-3.34593 + 12.4872i) q^{89} +(-1.60783 - 28.7627i) q^{90} +(1.76406 + 3.14453i) q^{91} +(-3.78945 + 2.18784i) q^{92} +(10.7100 + 10.1280i) q^{93} +0.317159 q^{94} +(-1.65301 - 2.86310i) q^{95} +(2.24870 + 7.54325i) q^{96} +(-10.3209 - 10.3209i) q^{97} +(-2.25121 + 0.603210i) q^{98} +(3.49163 - 16.7128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) $ 336 * q - 12 * q^6 + 36 * q^8	$ 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) $ 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.603210	−	2.25121i	−0.426534	−	1.59185i	−0.760550	−	0.649279i	$-0.775071\pi$
$2$	−0.603210	−	2.25121i	−0.426534	−	1.59185i	0.334016	−	0.942567i	$-0.391596\pi$
$3$	0.907564	+	1.47524i	0.523982	+	0.851729i
$3$	0.907564	+	1.47524i	0.523982	+	0.851729i
$4$	−2.97204	+	1.71591i	−1.48602	+	0.857954i
$5$	−1.06637	−	3.97976i	−0.476897	−	1.77980i	−0.614065	−	0.789255i	$-0.710467\pi$
$5$	−1.06637	−	3.97976i	−0.476897	−	1.77980i	0.137168	−	0.990548i	$-0.456200\pi$
$6$	2.77362	−	2.93300i	1.13233	−	1.19739i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	2.35963	+	2.35963i	0.834257	+	0.834257i
$9$	−1.35266	+	2.67775i	−0.450885	+	0.892582i
$10$	−8.31604	+	4.80127i	−2.62976	+	1.51829i
$11$	−5.49728	+	1.47299i	−1.65749	+	0.444124i	−0.961697	−	0.274115i	$-0.911615\pi$
$11$	−5.49728	+	1.47299i	−1.65749	+	0.444124i	−0.695796	+	0.718239i	$0.744948\pi$
$12$	−5.22869	−	2.82717i	−1.50939	−	0.816134i
$13$	−0.976138	+	3.47090i	−0.270732	+	0.962655i
$13$	−0.976138	+	3.47090i	−0.270732	+	0.962655i
$14$	−2.01838	−	1.16531i	−0.539435	−	0.311443i
$15$	4.90329	−	5.18504i	1.26602	−	1.33877i
$16$	0.456865	−	0.791313i	0.114216	−	0.197828i
$17$	0.220817	−	0.382467i	0.0535561	−	0.0927618i	−0.838004	−	0.545663i	$-0.816278\pi$
$17$	0.220817	−	0.382467i	0.0535561	−	0.0927618i	0.891561	+	0.452902i	$0.149611\pi$
$18$	6.84411	+	1.42987i	1.61317	+	0.337024i
$19$	0.775062	−	0.207677i	0.177812	−	0.0476445i	−0.168815	−	0.985648i	$-0.553994\pi$
$19$	0.775062	−	0.207677i	0.177812	−	0.0476445i	0.346626	+	0.938003i	$0.387327\pi$
$20$	9.99821	+	9.99821i	2.23567	+	2.23567i
$21$	1.68490	+	0.401407i	0.367674	+	0.0875941i
$22$	6.63203	+	11.4870i	1.41395	+	2.44904i
$23$	1.27503			0.265863			0.132931	−	0.991125i	$-0.457561\pi$
$23$	1.27503			0.265863			0.132931	+	0.991125i	$0.457561\pi$
$24$	−1.33950	+	5.62254i	−0.273425	+	1.14770i
$25$	−10.3712	+	5.98782i	−2.07424	+	1.19756i
$26$	8.40255	+	0.103809i	1.64788	+	0.0203586i
$27$	−5.17793	+	0.434735i	−0.996494	+	0.0836647i
$28$	−0.888219	+	3.31488i	−0.167858	+	0.626453i
$29$	−4.93302	−	2.84808i	−0.916040	−	0.528876i	−0.0336702	−	0.999433i	$-0.510720\pi$
$29$	−4.93302	−	2.84808i	−0.916040	−	0.528876i	−0.882369	+	0.470557i	$0.844053\pi$
$30$	−14.6303	−	7.91068i	−2.67112	−	1.44429i
$31$	8.22040	−	2.20265i	1.47643	−	0.395608i	0.571298	−	0.820743i	$-0.306440\pi$
$31$	8.22040	−	2.20265i	1.47643	−	0.395608i	0.905130	+	0.425135i	$0.139773\pi$
$32$	4.38964	+	1.17620i	0.775987	+	0.207925i
$33$	−7.16215	−	6.77297i	−1.24677	−	1.17902i
$34$	−0.994213	−	0.266399i	−0.170506	−	0.0456870i
$35$	−3.56816	−	2.06008i	−0.603128	−	0.348216i
$36$	−0.574617	−	10.2794i	−0.0957695	−	1.71323i
$37$	−10.4305	−	2.79484i	−1.71476	−	0.459468i	−0.738175	−	0.674609i	$-0.764312\pi$
$37$	−10.4305	−	2.79484i	−1.71476	−	0.459468i	−0.976583	+	0.215141i	$0.930979\pi$
$38$	−0.935051	−	1.61956i	−0.151685	−	0.262727i
$39$	−6.00631	+	1.71003i	−0.961780	+	0.273824i
$40$	6.87453	−	11.9070i	1.08696	−	1.88267i
$41$	0.839742	−	0.839742i	0.131146	−	0.131146i	−0.638487	−	0.769633i	$-0.720439\pi$
$41$	0.839742	−	0.839742i	0.131146	−	0.131146i	0.769633	+	0.638487i	$0.220439\pi$
$42$	−0.112695	−	4.03519i	−0.0173893	−	0.622643i
$43$			10.5095i			1.60269i	0.598204	+	0.801344i	$0.295881\pi$
$43$			10.5095i			1.60269i	−0.598204	+	0.801344i	$0.704119\pi$
$44$	13.8106	−	13.8106i	2.08203	−	2.08203i
$45$	12.0992	+	2.52777i	1.80365	+	0.376818i
$46$	−0.769114	−	2.87037i	−0.113400	−	0.423213i
$47$	−0.0352210	+	0.131446i	−0.00513751	+	0.0191734i	−0.968447	−	0.249220i	$-0.919826\pi$
$47$	−0.0352210	+	0.131446i	−0.00513751	+	0.0191734i	0.963309	+	0.268393i	$0.0864926\pi$
$48$	1.58201	−	0.0441826i	0.228343	−	0.00637720i
$49$		−	1.00000i		−	0.142857i
$50$	19.7359	+	19.7359i	2.79108	+	2.79108i
$51$	0.764635	−	0.0213548i	0.107070	−	0.00299028i
$52$	−3.05463	−	11.9906i	−0.423601	−	1.66280i
$53$		−	0.940462i		−	0.129182i	−0.997912	−	0.0645912i	$-0.979426\pi$
$53$		−	0.940462i		−	0.129182i	0.997912	−	0.0645912i	$-0.0205743\pi$
$54$	4.10206	+	11.3944i	0.558220	+	1.55058i
$55$	11.7243	+	20.3071i	1.58091	+	2.73821i
$56$	3.33703			0.445929
$57$	1.00979	+	0.954921i	0.133750	+	0.126482i
$58$	−3.43599	+	12.8233i	−0.451167	+	1.68378i
$59$	−1.70873	+	6.37705i	−0.222457	+	0.830222i	0.760950	+	0.648810i	$0.224733\pi$
$59$	−1.70873	+	6.37705i	−0.222457	+	0.830222i	−0.983407	+	0.181411i	$0.941933\pi$
$60$	−5.67573	+	23.8238i	−0.732733	+	3.07563i
$61$	−1.23929			−0.158675			−0.0793377	−	0.996848i	$-0.525281\pi$
$61$	−1.23929			−0.158675			−0.0793377	+	0.996848i	$0.525281\pi$
$62$	−9.91726	−	17.1772i	−1.25949	−	2.18151i
$63$	0.936980	+	2.84992i	0.118048	+	0.359057i
$64$		−	12.4190i		−	1.55237i
$65$	14.8543	+	0.183517i	1.84245	+	0.0227625i
$66$	−10.9271	+	20.2090i	−1.34503	+	2.48756i
$67$	−3.59577	−	3.59577i	−0.439294	−	0.439294i	0.452481	−	0.891774i	$-0.350539\pi$
$67$	−3.59577	−	3.59577i	−0.439294	−	0.439294i	−0.891774	+	0.452481i	$0.850539\pi$
$68$			1.51561i			0.183795i
$69$	1.15717	+	1.88098i	0.139307	+	0.226443i
$70$	−2.48532	+	9.27533i	−0.297052	+	1.10861i
$71$	0.243859	+	0.910095i	0.0289408	+	0.108008i	0.978885	−	0.204410i	$-0.0655276\pi$
$71$	0.243859	+	0.910095i	0.0289408	+	0.108008i	−0.949945	+	0.312418i	$0.898861\pi$
$72$	−9.51028	+	3.12673i	−1.12080	+	0.368488i
$73$	1.75591	−	1.75591i	0.205513	−	0.205513i	−0.596844	−	0.802357i	$-0.703579\pi$
$73$	1.75591	−	1.75591i	0.205513	−	0.205513i	0.802357	+	0.596844i	$0.203579\pi$
$74$			25.1671i			2.92561i
$75$	−18.2460	−	9.86568i	−2.10687	−	1.13919i
$76$	−1.94716	+	1.94716i	−0.223355	+	0.223355i
$77$	−2.84560	+	4.92873i	−0.324287	+	0.561681i
$78$	7.47271	+	12.4900i	0.846117	+	1.41421i
$79$	−0.384719	−	0.666354i	−0.0432843	−	0.0749706i	0.843572	−	0.537017i	$-0.180449\pi$
$79$	−0.384719	−	0.666354i	−0.0432843	−	0.0749706i	−0.886856	+	0.462046i	$0.847115\pi$
$80$	−3.63643	−	0.974377i	−0.406565	−	0.108939i
$81$	−5.34064	−	7.24414i	−0.593405	−	0.804904i
$82$	−2.39698	−	1.38390i	−0.264702	−	0.152826i
$83$	−15.6094	−	4.18253i	−1.71335	−	0.459092i	−0.737112	−	0.675771i	$-0.763811\pi$
$83$	−15.6094	−	4.18253i	−1.71335	−	0.459092i	−0.976243	+	0.216679i	$0.930478\pi$
$84$	−5.69635	+	1.69813i	−0.621523	+	0.185281i
$85$	−1.75760	−	0.470948i	−0.190638	−	0.0510814i
$86$	23.6592	−	6.33946i	2.55123	−	0.683601i
$87$	−0.275433	−	9.86220i	−0.0295295	−	1.05734i
$88$	−16.4473	−	9.49585i	−1.75329	−	1.01226i
$89$	−3.34593	+	12.4872i	−0.354668	+	1.32364i	0.526234	+	0.850340i	$0.323604\pi$
$89$	−3.34593	+	12.4872i	−0.354668	+	1.32364i	−0.880902	+	0.473299i	$0.843063\pi$
$90$	−1.60783	−	28.7627i	−0.169480	−	3.03185i
$91$	1.76406	+	3.14453i	0.184924	+	0.329636i
$92$	−3.78945	+	2.18784i	−0.395078	+	0.228098i
$93$	10.7100	+	10.1280i	1.11057	+	1.05023i
$94$	0.317159			0.0327125
$95$	−1.65301	−	2.86310i	−0.169595	−	0.293748i
$96$	2.24870	+	7.54325i	0.229507	+	0.769879i
$97$	−10.3209	−	10.3209i	−1.04793	−	1.04793i	−0.998792	−	0.0491389i	$-0.984352\pi$
$97$	−10.3209	−	10.3209i	−1.04793	−	1.04793i	−0.0491389	−	0.998792i	$-0.515648\pi$
$98$	−2.25121	+	0.603210i	−0.227407	+	0.0609334i
$99$	3.49163	−	16.7128i	0.350922	−	1.67970i
$100$	20.5491	−	35.5921i	2.05491	−	3.55921i
$101$	−5.55951	+	9.62935i	−0.553191	+	0.958156i	0.444850	+	0.895605i	$0.353257\pi$
$101$	−5.55951	+	9.62935i	−0.553191	+	0.958156i	−0.998042	+	0.0625508i	$0.980076\pi$
$102$	−0.509310	−	1.70847i	−0.0504292	−	0.169164i
$103$	−2.12493	−	1.22683i	−0.209375	−	0.120883i	0.391646	−	0.920116i	$-0.371906\pi$
$103$	−2.12493	−	1.22683i	−0.209375	−	0.120883i	−0.601021	+	0.799233i	$0.705239\pi$
$104$	−10.4934	+	5.88673i	−1.02896	+	0.577241i
$105$	−0.199226	−	7.13353i	−0.0194425	−	0.696161i
$106$	−2.11718	+	0.567296i	−0.205639	+	0.0551007i
$107$	10.3064	−	5.95039i	0.996355	−	0.575246i	0.0891875	−	0.996015i	$-0.471573\pi$
$107$	10.3064	−	5.95039i	0.996355	−	0.575246i	0.907168	+	0.420769i	$0.138240\pi$
$108$	14.6431	−	10.1769i	1.40903	−	0.979273i
$109$	2.08628	+	2.08628i	0.199829	+	0.199829i	0.799927	−	0.600098i	$-0.204872\pi$
$109$	2.08628	+	2.08628i	0.199829	+	0.199829i	−0.600098	+	0.799927i	$0.704872\pi$
$110$	38.6434	−	38.6434i	3.68450	−	3.68450i
$111$	−5.34327	−	17.9239i	−0.507160	−	1.70126i
$112$	−0.236491	−	0.882595i	−0.0223463	−	0.0833974i
$113$	0.650144	−	0.375361i	0.0611604	−	0.0353110i	−0.469108	−	0.883141i	$-0.655425\pi$
$113$	0.650144	−	0.375361i	0.0611604	−	0.0353110i	0.530268	+	0.847830i	$0.322091\pi$
$114$	1.54061	−	2.84927i	0.144292	−	0.266859i
$115$	−1.35966	−	5.07433i	−0.126789	−	0.473184i
$116$	19.5482			1.81500
$117$	−7.97381	−	7.30878i	−0.737179	−	0.675697i
$118$	15.3868			1.41647
$119$	−0.114303	−	0.426586i	−0.0104782	−	0.0391051i
$120$	23.8048	−	0.664823i	2.17307	−	0.0606898i
$121$	18.5241	−	10.6949i	1.68401	−	0.972265i
$122$	0.747555	+	2.78991i	0.0676805	+	0.252587i
$123$	2.00094	+	0.476700i	0.180419	+	0.0429826i
$124$	−20.6518	+	20.6518i	−1.85459	+	1.85459i
$125$	20.3228	+	20.3228i	1.81772	+	1.81772i
$126$	5.85059	−	3.82844i	0.521212	−	0.341065i
$127$	−3.05512	+	1.76388i	−0.271098	+	0.156519i	−0.629387	−	0.777092i	$-0.716694\pi$
$127$	−3.05512	+	1.76388i	−0.271098	+	0.156519i	0.358288	+	0.933611i	$0.383360\pi$
$128$	−19.1784	+	5.13885i	−1.69515	+	0.454214i
$129$	−15.5041	+	9.53807i	−1.36506	+	0.839780i
$130$	−8.54712	−	33.5508i	−0.749632	−	2.94260i
$131$	−12.3177	−	7.11165i	−1.07621	−	0.621347i	−0.146335	−	0.989235i	$-0.546748\pi$
$131$	−12.3177	−	7.11165i	−1.07621	−	0.621347i	−0.929870	+	0.367888i	$0.880081\pi$
$132$	32.9080	+	7.83994i	2.86427	+	0.682379i
$133$	0.401202	−	0.694902i	0.0347886	−	0.0602556i
$134$	−5.92584	+	10.2639i	−0.511915	+	0.886662i
$135$	7.25175	+	20.1434i	0.624131	+	1.73366i
$136$	1.42353	−	0.381434i	0.122067	−	0.0327077i
$137$	−10.6770	−	10.6770i	−0.912194	−	0.912194i	0.0842509	−	0.996445i	$-0.473150\pi$
$137$	−10.6770	−	10.6770i	−0.912194	−	0.912194i	−0.996445	+	0.0842509i	$0.973150\pi$
$138$	3.53646	−	3.73967i	0.301044	−	0.318342i
$139$	−10.8144	−	18.7310i	−0.917263	−	1.58875i	−0.803554	−	0.595232i	$-0.797060\pi$
$139$	−10.8144	−	18.7310i	−0.917263	−	1.58875i	−0.113709	−	0.993514i	$-0.536273\pi$
$140$	14.1396			1.19501
$141$	−0.225880	+	0.0673367i	−0.0190225	+	0.00567077i
$142$	1.90172	−	1.09796i	0.159589	−	0.0921386i
$143$	0.253494	−	20.5184i	0.0211982	−	1.71583i
$144$	1.50095	+	2.29374i	0.125080	+	0.191145i
$145$	−6.07424	+	22.6694i	−0.504438	+	1.88259i
$146$	−5.01210	−	2.89374i	−0.414804	−	0.239487i
$147$	1.47524	−	0.907564i	0.121676	−	0.0748546i
$148$	35.7955	−	9.59136i	2.94237	−	0.788405i
$149$	−8.57108	−	2.29662i	−0.702171	−	0.188146i	−0.109968	−	0.993935i	$-0.535075\pi$
$149$	−8.57108	−	2.29662i	−0.702171	−	0.188146i	−0.592203	+	0.805789i	$0.701741\pi$
$150$	−11.2036	+	47.0267i	−0.914767	+	3.83971i
$151$	18.9915	+	5.08876i	1.54551	+	0.414117i	0.928040	−	0.372480i	$-0.121493\pi$
$151$	18.9915	+	5.08876i	1.54551	+	0.414117i	0.617466	+	0.786597i	$0.288159\pi$
$152$	2.31891	+	1.33882i	0.188088	+	0.108593i
$153$	0.725459	+	1.10864i	0.0586499	+	0.0896281i
$154$	12.8121	+	3.43299i	1.03243	+	0.276639i
$155$	−17.5320	−	30.3664i	−1.40821	−	2.43909i
$156$	14.9168	−	15.3886i	1.19430	−	1.23207i
$157$	−0.938535	+	1.62559i	−0.0749033	+	0.129736i	−0.901044	−	0.433727i	$-0.857198\pi$
$157$	−0.938535	+	1.62559i	−0.0749033	+	0.129736i	0.826141	+	0.563464i	$0.190531\pi$
$158$	−1.26804	+	1.26804i	−0.100880	+	0.100880i
$159$	1.38741	−	0.853529i	0.110028	−	0.0676893i
$160$		−	18.7240i		−	1.48026i
$161$	0.901585	−	0.901585i	0.0710549	−	0.0710549i
$162$	−13.0866	+	16.3927i	−1.02818	+	1.28793i
$163$	−3.99324	−	14.9030i	−0.312775	−	1.16729i	−0.926043	−	0.377418i	$-0.876812\pi$
$163$	−3.99324	−	14.9030i	−0.312775	−	1.16729i	0.613268	−	0.789875i	$-0.289855\pi$
$164$	−1.05483	+	3.93667i	−0.0823681	+	0.307402i
$165$	−19.3173	+	35.7262i	−1.50385	+	2.78128i
$166$			37.6630i			2.92322i
$167$	4.74480	+	4.74480i	0.367164	+	0.367164i	0.866442	−	0.499278i	$-0.166401\pi$
$167$	4.74480	+	4.74480i	0.367164	+	0.367164i	−0.499278	+	0.866442i	$0.666401\pi$
$168$	3.02857	+	4.92291i	0.233659	+	0.379811i
$169$	−11.0943	−	6.77616i	−0.853408	−	0.521243i
$170$			4.24081i			0.325255i
$171$	−0.492286	+	2.35634i	−0.0376460	+	0.180194i
$172$	−18.0334	−	31.2347i	−1.37503	−	2.38163i
$173$	4.24515			0.322753			0.161377	−	0.986893i	$-0.448407\pi$
$173$	4.24515			0.322753			0.161377	+	0.986893i	$0.448407\pi$
$174$	−22.0358	+	6.56904i	−1.67053	+	0.497998i
$175$	−3.09953	+	11.5676i	−0.234302	+	0.874427i
$176$	−1.34592	+	5.02303i	−0.101452	+	0.378625i
$177$	−10.9585	+	3.26680i	−0.823688	+	0.245548i
$178$	30.1296			2.25831
$179$	4.22394	+	7.31609i	0.315712	+	0.546830i	0.979589	−	0.201012i	$-0.0644232\pi$
$179$	4.22394	+	7.31609i	0.315712	+	0.546830i	−0.663876	+	0.747842i	$0.731090\pi$
$180$	−40.2968	+	13.2485i	−3.00355	+	0.987486i
$181$		−	11.5795i		−	0.860695i	−0.902663	−	0.430347i	$-0.858391\pi$
$181$		−	11.5795i		−	0.860695i	0.902663	−	0.430347i	$-0.141609\pi$
$182$	6.01490	−	5.86810i	0.445854	−	0.434972i
$183$	−1.12474	−	1.82825i	−0.0831431	−	0.135148i
$184$	3.00861	+	3.00861i	0.221798	+	0.221798i
$185$			44.4911i			3.27105i
$186$	16.3399	−	30.2197i	1.19810	−	2.21582i
$187$	−0.650524	+	2.42779i	−0.0475711	+	0.177538i
$188$	−0.120872	−	0.451100i	−0.00881549	−	0.0328999i
$189$	−3.35395	+	3.96876i	−0.243964	+	0.288685i
$190$	−5.44833	+	5.44833i	−0.395264	+	0.395264i
$191$		−	10.4113i		−	0.753332i	−0.926349	−	0.376666i	$-0.877070\pi$
$191$		−	10.4113i		−	0.753332i	0.926349	−	0.376666i	$-0.122930\pi$
$192$	18.3209	−	11.2710i	1.32220	−	0.813415i
$193$	4.66494	−	4.66494i	0.335789	−	0.335789i	−0.518991	−	0.854780i	$-0.673692\pi$
$193$	4.66494	−	4.66494i	0.335789	−	0.335789i	0.854780	+	0.518991i	$0.173692\pi$
$194$	−17.0089	+	29.4603i	−1.22117	+	2.11512i
$195$	13.2105	+	22.0802i	0.946022	+	1.58119i
$196$	1.71591	+	2.97204i	0.122565	+	0.212289i
$197$	−1.90867	−	0.511426i	−0.135987	−	0.0364376i	0.190184	−	0.981749i	$-0.439092\pi$
$197$	−1.90867	−	0.511426i	−0.135987	−	0.0364376i	−0.326170	+	0.945311i	$0.605758\pi$
$198$	−39.7302	+	2.22091i	−2.82350	+	0.157833i
$199$	−10.0886	−	5.82465i	−0.715162	−	0.412899i	0.0978077	−	0.995205i	$-0.468817\pi$
$199$	−10.0886	−	5.82465i	−0.715162	−	0.412899i	−0.812969	+	0.582307i	$0.802150\pi$
$200$	−38.6014	−	10.3432i	−2.72953	−	0.731375i
$201$	2.04123	−	8.56802i	0.143977	−	0.604341i
$202$	25.0312	+	6.70710i	1.76119	+	0.471910i
$203$	−5.50207	+	1.47428i	−0.386170	+	0.103474i
$204$	−2.23588	+	1.37551i	−0.156543	+	0.0963051i
$205$	−4.23745	−	2.44649i	−0.295956	−	0.170870i
$206$	−1.48007	+	5.52370i	−0.103121	+	0.384854i
$207$	−1.72468	+	3.41422i	−0.119874	+	0.237304i
$208$	2.30061	+	2.35816i	0.159518	+	0.163509i
$209$	−3.95483	+	2.28332i	−0.273561	+	0.157941i
$210$	−15.9389	+	4.75152i	−1.09989	+	0.327886i
$211$	7.79294			0.536488			0.268244	−	0.963351i	$-0.413557\pi$
$211$	7.79294			0.536488			0.268244	+	0.963351i	$0.413557\pi$
$212$	1.61375	+	2.79509i	0.110833	+	0.191968i
$213$	−1.12129	+	1.18572i	−0.0768295	+	0.0812442i
$214$	−19.6125	−	19.6125i	−1.34068	−	1.34068i
$215$	41.8254	−	11.2071i	2.85247	−	0.764317i
$216$	−13.2438	−	11.1922i	−0.901130	−	0.761534i
$217$	4.25519	−	7.37021i	0.288861	−	0.500323i
$218$	3.43819	−	5.95512i	0.232864	−	0.403332i
$219$	4.18398	+	0.996784i	0.282727	+	0.0673564i
$220$	−69.6903	−	40.2357i	−4.69852	−	2.71269i
$221$	1.11196	+	1.13978i	0.0747983	+	0.0766696i
$222$	−37.1274	+	22.8407i	−2.49183	+	1.53297i
$223$	−7.34330	+	1.96763i	−0.491744	+	0.131762i	−0.496166	−	0.868228i	$-0.665259\pi$
$223$	−7.34330	+	1.96763i	−0.491744	+	0.131762i	0.00442197	+	0.999990i	$0.498592\pi$
$224$	3.93565	−	2.27225i	0.262961	−	0.151821i
$225$	−2.00518	−	35.8709i	−0.133679	−	2.39140i
$226$	−1.23719	−	1.23719i	−0.0822966	−	0.0822966i
$227$	−3.42011	+	3.42011i	−0.227000	+	0.227000i	−0.811438	−	0.584438i	$-0.801315\pi$
$227$	−3.42011	+	3.42011i	−0.227000	+	0.227000i	0.584438	+	0.811438i	$0.301315\pi$
$228$	−4.63970	−	1.10535i	−0.307272	−	0.0732039i
$229$	4.83242	+	18.0348i	0.319335	+	1.19177i	0.919885	+	0.392188i	$0.128282\pi$
$229$	4.83242	+	18.0348i	0.319335	+	1.19177i	−0.600550	+	0.799587i	$0.705052\pi$
$230$	−10.6032	+	6.12178i	−0.699156	+	0.403658i
$231$	−9.85362	+	0.275193i	−0.648320	+	0.0181064i
$232$	−4.91970	−	18.3606i	−0.322994	−	1.20543i
$233$	−3.15485			−0.206681			−0.103341	−	0.994646i	$-0.532953\pi$
$233$	−3.15485			−0.206681			−0.103341	+	0.994646i	$0.532953\pi$
$234$	−11.6437	+	22.3595i	−0.761175	+	1.46168i
$235$	0.560684			0.0365750
$236$	−5.86404	−	21.8849i	−0.381716	−	1.42458i
$237$	0.633873	−	1.17231i	0.0411745	−	0.0761498i
$238$	−0.891387	+	0.514642i	−0.0577800	+	0.0333593i
$239$	0.171064	+	0.638421i	0.0110652	+	0.0412960i	0.971238	−	0.238112i	$-0.0765285\pi$
$239$	0.171064	+	0.638421i	0.0110652	+	0.0412960i	−0.960172	+	0.279408i	$0.909862\pi$
$240$	−1.86285	−	6.24890i	−0.120246	−	0.403365i
$241$	1.67347	−	1.67347i	0.107798	−	0.107798i	−0.651151	−	0.758948i	$-0.725713\pi$
$241$	1.67347	−	1.67347i	0.107798	−	0.107798i	0.758948	+	0.651151i	$0.225713\pi$
$242$	−35.2505	−	35.2505i	−2.26598	−	2.26598i
$243$	5.83986	−	14.4532i	0.374627	−	0.927176i
$244$	3.68323	−	2.12652i	0.235795	−	0.136136i
$245$	−3.97976	+	1.06637i	−0.254258	+	0.0681281i
$246$	−0.133834	−	4.79209i	−0.00853294	−	0.305532i
$247$	−0.0357401	+	2.89289i	−0.00227409	+	0.184070i
$248$	24.5946	+	14.1997i	1.56176	+	0.901682i
$249$	−7.99631	−	26.8235i	−0.506745	−	1.69987i
$250$	33.4919	−	58.0097i	2.11822	−	3.66886i
$251$	−6.05835	+	10.4934i	−0.382399	+	0.662335i	−0.991405	−	0.130831i	$-0.958235\pi$
$251$	−6.05835	+	10.4934i	−0.382399	+	0.662335i	0.609005	+	0.793166i	$0.291569\pi$
$252$	−7.67495	−	6.86232i	−0.483476	−	0.432285i
$253$	−7.00922	+	1.87812i	−0.440666	+	0.118076i
$254$	5.81374	+	5.81374i	0.364786	+	0.364786i
$255$	−0.900374	−	3.02029i	−0.0563836	−	0.189138i
$256$	10.7183	+	18.5646i	0.669894	+	1.16029i
$257$	4.93683			0.307951			0.153975	−	0.988075i	$-0.450792\pi$
$257$	4.93683			0.307951			0.153975	+	0.988075i	$0.450792\pi$
$258$	30.8244	+	29.1495i	1.91904	+	1.81477i
$259$	−9.35170	+	5.39921i	−0.581087	+	0.335490i
$260$	−44.4624	+	24.9432i	−2.75744	+	1.54691i
$261$	14.2991	−	9.35691i	0.885094	−	0.579178i
$262$	−8.57964	+	32.0196i	−0.530052	+	1.97818i
$263$	3.67269	+	2.12043i	0.226468	+	0.130751i	0.608942	−	0.793215i	$-0.291594\pi$
$263$	3.67269	+	2.12043i	0.226468	+	0.130751i	−0.382474	+	0.923966i	$0.624928\pi$
$264$	−0.918327	−	32.8818i	−0.0565191	−	2.02373i
$265$	−3.74281	+	1.00288i	−0.229919	+	0.0616067i
$266$	−1.80638	−	0.484018i	−0.110756	−	0.0296771i
$267$	−21.4582	+	6.39687i	−1.31322	+	0.391482i
$268$	16.8568	+	4.51677i	1.02969	+	0.275905i
$269$	6.51830	+	3.76334i	0.397428	+	0.229455i	0.685374	−	0.728192i	$-0.259639\pi$
$269$	6.51830	+	3.76334i	0.397428	+	0.229455i	−0.287946	+	0.957647i	$0.592972\pi$
$270$	40.9726	−	28.4759i	2.49351	−	1.73299i
$271$	−10.9903	−	2.94484i	−0.667613	−	0.178886i	−0.0909336	−	0.995857i	$-0.528985\pi$
$271$	−10.9903	−	2.94484i	−0.667613	−	0.178886i	−0.576679	+	0.816971i	$0.695652\pi$
$272$	−0.201767	−	0.349471i	−0.0122339	−	0.0211898i
$273$	−3.03793	+	5.45628i	−0.183864	+	0.330229i
$274$	−17.5956	+	30.4765i	−1.06299	+	1.84115i
$275$	48.1935	−	48.1935i	2.90618	−	2.90618i
$276$	−6.66676	−	3.60474i	−0.401292	−	0.216980i
$277$			10.0786i			0.605566i	0.953059	+	0.302783i	$0.0979158\pi$
$277$			10.0786i			0.605566i	−0.953059	+	0.302783i	$0.902084\pi$
$278$	−35.6442	+	35.6442i	−2.13780	+	2.13780i
$279$	−5.22124	+	24.9916i	−0.312588	+	1.49621i
$280$	−3.55852	−	13.2806i	−0.212662	−	0.793666i
$281$	3.28568	−	12.2623i	0.196007	−	0.731509i	−0.795997	−	0.605301i	$-0.793053\pi$
$281$	3.28568	−	12.2623i	0.196007	−	0.731509i	0.992004	−	0.126208i	$-0.0402806\pi$
$282$	0.287842	+	0.467886i	0.0171408	+	0.0278622i
$283$			0.966309i			0.0574411i	0.999587	+	0.0287205i	$0.00914329\pi$
$283$			0.966309i			0.0574411i	−0.999587	+	0.0287205i	$0.990857\pi$
$284$	−2.28640	−	2.28640i	−0.135673	−	0.135673i
$285$	2.72354	−	5.03703i	0.161329	−	0.298368i
$286$	−46.3441	+	11.8062i	−2.74038	+	0.698117i
$287$		−	1.18757i		−	0.0701003i
$288$	−9.08725	+	10.1634i	−0.535471	+	0.598881i
$289$	8.40248	+	14.5535i	0.494263	+	0.856089i
$290$	54.6976			3.21195
$291$	5.85893	−	24.5927i	0.343456	−	1.44165i
$292$	−2.20565	+	8.23160i	−0.129076	+	0.481718i
$293$	−0.513514	+	1.91646i	−0.0299998	+	0.111961i	−0.979302	−	0.202404i	$-0.935125\pi$
$293$	−0.513514	+	1.91646i	−0.0299998	+	0.111961i	0.949302	+	0.314364i	$0.101791\pi$
$294$	−2.93300	−	2.77362i	−0.171056	−	0.161761i
$295$	27.2013			1.58372
$296$	−18.0173	−	31.2069i	−1.04723	−	1.81386i
$297$	27.8242	−	10.0169i	1.61452	−	0.581240i
$298$			20.6807i			1.19800i
$299$	−1.24461	+	4.42552i	−0.0719776	+	0.255934i
$300$	71.1565	−	1.98727i	4.10822	−	0.114735i
$301$	7.43136	+	7.43136i	0.428336	+	0.428336i
$302$		−	45.8235i		−	2.63684i
$303$	−19.2512	+	0.537650i	−1.10595	+	0.0308872i
$304$	0.189761	−	0.708198i	0.0108835	−	0.0406179i
$305$	1.32155	+	4.93210i	0.0756718	+	0.282411i
$306$	2.05818	−	2.30190i	0.117658	−	0.131591i
$307$	4.75768	−	4.75768i	0.271535	−	0.271535i	−0.558183	−	0.829718i	$-0.688501\pi$
$307$	4.75768	−	4.75768i	0.271535	−	0.271535i	0.829718	+	0.558183i	$0.188501\pi$
$308$		−	19.5312i		−	1.11289i
$309$	−0.118644	−	4.24820i	−0.00674944	−	0.241672i
$310$	−57.7857	+	57.7857i	−3.28200	+	3.28200i
$311$	16.3934	−	28.3942i	0.929583	−	1.61009i	0.145564	−	0.989349i	$-0.453500\pi$
$311$	16.3934	−	28.3942i	0.929583	−	1.61009i	0.784019	−	0.620736i	$-0.213166\pi$
$312$	−18.2077	−	10.1377i	−1.03081	−	0.573932i
$313$	12.3302	+	21.3565i	0.696942	+	1.20714i	0.969522	+	0.245006i	$0.0787899\pi$
$313$	12.3302	+	21.3565i	0.696942	+	1.20714i	−0.272579	+	0.962133i	$0.587877\pi$
$314$	4.22568	+	1.13227i	0.238469	+	0.0638976i
$315$	10.3428	−	6.76804i	0.582753	−	0.381336i
$316$	2.28680	+	1.32029i	0.128643	+	0.0742719i
$317$	20.8539	+	5.58778i	1.17127	+	0.313841i	0.791459	−	0.611223i	$-0.209322\pi$
$317$	20.8539	+	5.58778i	1.17127	+	0.313841i	0.379812	+	0.925064i	$0.375989\pi$
$318$	−2.75837	−	2.60849i	−0.154682	−	0.146277i
$319$	31.3134	+	8.39041i	1.75322	+	0.469773i
$320$	−49.4245	+	13.2433i	−2.76292	+	0.740321i
$321$	18.1319	+	9.80401i	1.01203	+	0.547206i
$322$	−2.57350	−	1.48581i	−0.143416	−	0.0828011i
$323$	0.0917175	−	0.342294i	0.00510330	−	0.0190458i
$324$	28.3029	+	12.3658i	1.57238	+	0.686990i
$325$	−10.6594	−	41.8424i	−0.591278	−	2.32100i
$326$	−31.1410	+	17.9793i	−1.72474	+	0.995780i
$327$	−1.18433	+	4.97119i	−0.0654935	+	0.274908i
$328$	3.96297			0.218818
$329$	0.0680417	+	0.117852i	0.00375126	+	0.00649737i
$330$	92.0795	+	21.9369i	5.06881	+	1.20758i
$331$	−14.3033	−	14.3033i	−0.786181	−	0.786181i	0.194685	−	0.980866i	$-0.437632\pi$
$331$	−14.3033	−	14.3033i	−0.786181	−	0.786181i	−0.980866	+	0.194685i	$0.937632\pi$
$332$	53.5686	−	14.3537i	2.93996	−	0.787760i
$333$	21.5927	−	24.1497i	1.18327	−	1.32339i
$334$	7.81944	−	13.5437i	0.427861	−	0.741076i
$335$	−10.4759	+	18.1448i	−0.572358	+	0.991354i
$336$	1.08741	−	1.14989i	0.0593230	−	0.0627317i
$337$	13.9310	+	8.04304i	0.758867	+	0.438132i	0.828889	−	0.559413i	$-0.188973\pi$
$337$	13.9310	+	8.04304i	0.758867	+	0.438132i	−0.0700215	+	0.997545i	$0.522307\pi$
$338$	−8.56236	+	29.0631i	−0.465731	+	1.58082i
$339$	1.14379	+	0.618453i	0.0621223	+	0.0335898i
$340$	6.03176	−	1.61621i	0.327118	−	0.0876510i
$341$	−41.9454	+	24.2172i	−2.27147	+	1.31143i
$342$	5.60156	−	0.313127i	0.302898	−	0.0169319i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−24.7986	+	24.7986i	−1.33705	+	1.33705i
$345$	6.25186	−	6.61110i	0.336589	−	0.355930i
$346$	−2.56072	−	9.55674i	−0.137665	−	0.513774i
$347$	−19.0733	+	11.0120i	−1.02391	+	0.591154i	−0.915234	−	0.402923i	$-0.867994\pi$
$347$	−19.0733	+	11.0120i	−1.02391	+	0.591154i	−0.108675	+	0.994077i	$0.534661\pi$
$348$	17.7412	+	28.8382i	0.951030	+	1.54589i
$349$	0.209191	+	0.780712i	0.0111977	+	0.0417906i	0.971299	−	0.237863i	$-0.0764470\pi$
$349$	0.209191	+	0.780712i	0.0111977	+	0.0417906i	−0.960101	+	0.279654i	$0.909780\pi$
$350$	27.9108			1.49189
$351$	3.54546	−	18.3965i	0.189242	−	0.981930i
$352$	−25.8636			−1.37854
$353$	−3.35479	−	12.5202i	−0.178557	−	0.666385i	−0.995918	−	0.0902589i	$-0.971231\pi$
$353$	−3.35479	−	12.5202i	−0.178557	−	0.666385i	0.817361	−	0.576126i	$-0.195436\pi$
$354$	13.9645	+	22.6992i	0.742206	+	1.20645i
$355$	3.36192	−	1.94100i	0.178432	−	0.103018i
$356$	−11.4826	−	42.8537i	−0.608578	−	2.27124i
$357$	0.525579	−	0.555779i	0.0278166	−	0.0294149i
$358$	13.9221	−	13.9221i	0.735808	−	0.735808i
$359$	−25.4927	−	25.4927i	−1.34545	−	1.34545i	−0.890530	−	0.454925i	$-0.849666\pi$
$359$	−25.4927	−	25.4927i	−1.34545	−	1.34545i	−0.454925	−	0.890530i	$-0.650334\pi$
$360$	22.5851	+	34.5144i	1.19034	+	1.81907i
$361$	−15.8969	+	9.17807i	−0.836678	+	0.483057i
$362$	−26.0678	+	6.98485i	−1.37009	+	0.367116i
$363$	32.5894	+	17.6212i	1.71050	+	0.924873i
$364$	−10.6386	−	6.31870i	−0.557614	−	0.331190i
$365$	−8.86054	−	5.11564i	−0.463782	−	0.267765i
$366$	−3.43733	+	3.63485i	−0.179672	+	0.189997i
$367$	5.36860	−	9.29869i	0.280239	−	0.485388i	−0.691205	−	0.722659i	$-0.742920\pi$
$367$	5.36860	−	9.29869i	0.280239	−	0.485388i	0.971443	+	0.237271i	$0.0762530\pi$
$368$	0.582518	−	1.00895i	0.0303659	−	0.0525952i
$369$	1.11273	+	3.38450i	0.0579266	+	0.176190i
$370$	100.159	−	26.8375i	5.20701	−	1.39521i
$371$	−0.665007	−	0.665007i	−0.0345255	−	0.0345255i
$372$	−49.2092	−	11.7235i	−2.55138	−	0.607836i
$373$	7.66188	+	13.2708i	0.396717	+	0.687134i	0.993319	−	0.115404i	$-0.0368161\pi$
$373$	7.66188	+	13.2708i	0.396717	+	0.687134i	−0.596602	+	0.802537i	$0.703483\pi$
$374$	5.85787			0.302903
$375$	−11.5367	+	48.4251i	−0.595753	+	2.50066i
$376$	−0.393274	+	0.227057i	−0.0202816	+	0.0117096i
$377$	14.7007	−	14.3419i	0.757126	−	0.738646i
$378$	10.9576	+	5.15645i	0.563601	+	0.265219i
$379$	2.58775	−	9.65760i	0.132924	−	0.496077i	−0.867074	−	0.498179i	$-0.834002\pi$
$379$	2.58775	−	9.65760i	0.132924	−	0.496077i	0.999998	+	0.00210148i	$0.000668924\pi$
$380$	9.82564	+	5.67283i	0.504045	+	0.291010i
$381$	−5.37485	−	2.90620i	−0.275362	−	0.148889i
$382$	−23.4379	+	6.28017i	−1.19919	+	0.321322i
$383$	−30.6057	−	8.20078i	−1.56388	−	0.419040i	−0.629990	−	0.776603i	$-0.716941\pi$
$383$	−30.6057	−	8.20078i	−1.56388	−	0.419040i	−0.933889	+	0.357563i	$0.883608\pi$
$384$	−24.9867	−	23.6289i	−1.27510	−	1.20581i
$385$	22.6496	+	6.06895i	1.15433	+	0.309302i
$386$	−13.3157	−	7.68782i	−0.677751	−	0.391300i
$387$	−28.1418	−	14.2158i	−1.43053	−	0.722629i
$388$	48.3839	+	12.9644i	2.45632	+	0.658170i
$389$	−3.79214	−	6.56817i	−0.192269	−	0.333020i	0.753733	−	0.657181i	$-0.228251\pi$
$389$	−3.79214	−	6.56817i	−0.192269	−	0.333020i	−0.946002	+	0.324161i	$0.894918\pi$
$390$	41.7384	−	43.0586i	2.11351	−	2.18036i
$391$	0.281550	−	0.487658i	0.0142386	−	0.0246619i
$392$	2.35963	−	2.35963i	0.119180	−	0.119180i
$393$	−0.687754	−	24.6259i	−0.0346926	−	1.24221i
$394$			4.60531i			0.232012i
$395$	−2.24167	+	2.24167i	−0.112791	+	0.112791i
$396$	18.3003	+	55.6624i	0.919625	+	2.79714i
$397$	6.10366	+	22.7792i	0.306334	+	1.14325i	0.931791	+	0.362995i	$0.118246\pi$
$397$	6.10366	+	22.7792i	0.306334	+	1.14325i	−0.625457	+	0.780259i	$0.715087\pi$
$398$	−7.02698	+	26.2251i	−0.352231	+	1.31454i
$399$	1.38926	−	0.0387995i	0.0695501	−	0.00194240i
$400$			10.9425i			0.547125i
$401$	13.5726	+	13.5726i	0.677786	+	0.677786i	0.959499	−	0.281713i	$-0.0909026\pi$
$401$	13.5726	+	13.5726i	0.677786	+	0.677786i	−0.281713	+	0.959499i	$0.590903\pi$
$402$	−20.5197	+	0.573077i	−1.02343	+	0.0285825i
$403$	−0.379064	+	30.6823i	−0.0188825	+	1.52839i
$404$		−	38.1584i		−	1.89845i
$405$	−23.1348	+	28.9794i	−1.14958	+	1.44000i
$406$	6.63782	+	11.4970i	0.329429	+	0.570588i
$407$	61.4560			3.04626
$408$	1.85465	+	1.75387i	0.0918189	+	0.0868295i
$409$	−2.06105	+	7.69195i	−0.101912	+	0.380342i	−0.997977	−	0.0635822i	$-0.979748\pi$
$409$	−2.06105	+	7.69195i	−0.101912	+	0.380342i	0.896064	+	0.443925i	$0.146414\pi$
$410$	−2.95150	+	11.0151i	−0.145764	+	0.543999i
$411$	6.06104	−	25.4411i	0.298969	−	1.25492i
$412$	8.42049			0.414848
$413$	3.30101	+	5.71751i	0.162432	+	0.281340i
$414$	8.72647	+	1.82313i	0.428883	+	0.0896022i
$415$			66.5818i			3.26837i
$416$	−8.36737	+	14.0879i	−0.410244	+	0.690715i
$417$	17.8180	−	32.9534i	0.872552	−	1.61373i
$418$	7.52584	+	7.52584i	0.368101	+	0.368101i
$419$			26.4603i			1.29267i	0.763054	+	0.646335i	$0.223699\pi$
$419$			26.4603i			1.29267i	−0.763054	+	0.646335i	$0.776301\pi$
$420$	12.8326	+	20.8593i	0.626166	+	1.01783i
$421$	−3.62287	+	13.5207i	−0.176568	+	0.658960i	0.819711	+	0.572777i	$0.194134\pi$
$421$	−3.62287	+	13.5207i	−0.176568	+	0.658960i	−0.996279	+	0.0861836i	$0.972533\pi$
$422$	−4.70078	−	17.5436i	−0.228830	−	0.854007i
$423$	−0.304338	−	0.272115i	−0.0147974	−	0.0132307i
$424$	2.21915	−	2.21915i	0.107771	−	0.107771i
$425$			5.28886i			0.256547i
$426$	3.34568	+	1.80902i	0.162099	+	0.0876474i
$427$	−0.876314	+	0.876314i	−0.0424078	+	0.0424078i
$428$	−20.4207	+	35.3696i	−0.987069	+	1.70965i
$429$	30.4995	−	18.2478i	1.47253	−	0.881010i
$430$	−50.4590	−	87.3976i	−2.43335	−	4.21469i
$431$	−11.0801	−	2.96891i	−0.533710	−	0.143007i	−0.0181092	−	0.999836i	$-0.505765\pi$
$431$	−11.0801	−	2.96891i	−0.533710	−	0.143007i	−0.515601	+	0.856829i	$0.672431\pi$
$432$	−2.02161	+	4.29598i	−0.0972645	+	0.206691i
$433$	3.01778	+	1.74232i	0.145025	+	0.0837304i	0.570757	−	0.821119i	$-0.306650\pi$
$433$	3.01778	+	1.74232i	0.145025	+	0.0837304i	−0.425732	+	0.904850i	$0.639983\pi$
$434$	−19.1587	−	5.13355i	−0.919646	−	0.246418i
$435$	−38.9555	+	11.6130i	−1.86777	+	0.556798i
$436$	−9.78037	−	2.62064i	−0.468395	−	0.125506i
$437$	0.988231	−	0.264796i	0.0472735	−	0.0126669i
$438$	−0.279848	−	10.0203i	−0.0133717	−	0.478788i
$439$	21.3236	+	12.3112i	1.01772	+	0.587580i	0.913442	−	0.406969i	$-0.133414\pi$
$439$	21.3236	+	12.3112i	1.01772	+	0.587580i	0.104276	+	0.994548i	$0.466748\pi$
$440$	−20.2523	+	75.5825i	−0.965489	+	3.60325i
$441$	2.67775	+	1.35266i	0.127512	+	0.0644122i
$442$	1.89513	−	3.19077i	0.0901422	−	0.151770i
$443$	18.9262	−	10.9270i	0.899209	−	0.519159i	0.0222656	−	0.999752i	$-0.492912\pi$
$443$	18.9262	−	10.9270i	0.899209	−	0.519159i	0.876944	+	0.480593i	$0.159579\pi$
$444$	46.6362	+	44.1020i	2.21326	+	2.09299i
$445$	53.2640			2.52496
$446$	8.85911	+	15.3444i	0.419491	+	0.726579i
$447$	−4.39075	−	14.7287i	−0.207675	−	0.696644i
$448$	−8.78154	−	8.78154i	−0.414889	−	0.414889i
$449$	17.7503	−	4.75617i	0.837686	−	0.224457i	0.185622	−	0.982621i	$-0.440570\pi$
$449$	17.7503	−	4.75617i	0.837686	−	0.224457i	0.652064	+	0.758164i	$0.273903\pi$
$450$	−79.5435	+	26.1518i	−3.74972	+	1.23281i
$451$	−3.37936	+	5.85323i	−0.159128	+	0.275618i
$452$	−1.28817	+	2.23117i	−0.0605904	+	0.104946i
$453$	9.72887	+	32.6354i	0.457102	+	1.53334i
$454$	9.76243	+	5.63634i	0.458173	+	0.264527i
$455$	10.6333	−	10.3738i	0.498498	−	0.486331i
$456$	0.129475	+	4.63601i	0.00606322	+	0.217101i
$457$	4.51621	−	1.21012i	0.211259	−	0.0566068i	−0.151637	−	0.988436i	$-0.548455\pi$
$457$	4.51621	−	1.21012i	0.211259	−	0.0566068i	0.362897	+	0.931829i	$0.381788\pi$
$458$	37.6852	−	21.7576i	1.76092	−	1.01666i
$459$	−0.977106	+	2.07638i	−0.0456074	+	0.0969173i
$460$	12.7481	+	12.7481i	0.594381	+	0.594381i
$461$	−3.30628	+	3.30628i	−0.153989	+	0.153989i	−0.779897	−	0.625908i	$-0.784729\pi$
$461$	−3.30628	+	3.30628i	−0.153989	+	0.153989i	0.625908	+	0.779897i	$0.284729\pi$
$462$	6.56332	+	22.0166i	0.305353	+	1.02430i
$463$	−4.24115	−	15.8282i	−0.197103	−	0.735598i	−0.991712	−	0.128477i	$-0.958991\pi$
$463$	−4.24115	−	15.8282i	−0.197103	−	0.735598i	0.794610	−	0.607121i	$-0.207676\pi$
$464$	−4.50745	+	2.60238i	−0.209253	+	0.120812i
$465$	28.8862	−	53.4234i	1.33957	−	2.47745i
$466$	1.90304	+	7.10225i	0.0881567	+	0.329005i
$467$	20.3524			0.941795			0.470898	−	0.882188i	$-0.343930\pi$
$467$	20.3524			0.941795			0.470898	+	0.882188i	$0.343930\pi$
$468$	36.2397	+	8.03967i	1.67518	+	0.371634i
$469$	−5.08519			−0.234812
$470$	−0.338210	−	1.26222i	−0.0156005	−	0.0582218i
$471$	−3.24991	+	0.0907640i	−0.149748	+	0.00418218i
$472$	−19.0795	+	11.0155i	−0.878205	+	0.507032i
$473$	−15.4805	−	57.7738i	−0.711792	−	2.65644i
$474$	−3.02148	−	0.719832i	−0.138781	−	0.0330630i
$475$	−6.79480	+	6.79480i	−0.311767	+	0.311767i
$476$	1.07170	+	1.07170i	0.0491212	+	0.0491212i
$477$	2.51832	+	1.27212i	0.115306	+	0.0582465i
$478$	1.33403	−	0.770205i	0.0610173	−	0.0352283i
$479$	−27.5260	+	7.37557i	−1.25769	+	0.336998i	−0.825304	−	0.564688i	$-0.808996\pi$
$479$	−27.5260	+	7.37557i	−1.25769	+	0.336998i	−0.432390	+	0.901686i	$0.642330\pi$
$480$	27.6224	−	16.9932i	1.26078	−	0.775631i
$481$	19.8822	−	33.4750i	0.906549	−	1.52633i
$482$	−4.77679	−	2.75788i	−0.217577	−	0.125618i
$483$	2.14830	+	0.511807i	0.0977510	+	0.0232880i
$484$	−36.7030	+	63.5714i	−1.66832	+	2.88961i
$485$	−30.0688	+	52.0808i	−1.36536	+	2.36487i
$486$	−36.0600	−	4.42841i	−1.63571	−	0.200877i
$487$	14.1496	−	3.79137i	0.641180	−	0.171804i	0.0764420	−	0.997074i	$-0.475644\pi$
$487$	14.1496	−	3.79137i	0.641180	−	0.171804i	0.564738	+	0.825270i	$0.308977\pi$
$488$	−2.92428	−	2.92428i	−0.132376	−	0.132376i
$489$	18.3613	−	19.4164i	0.830329	−	0.878040i
$490$	4.80127	+	8.31604i	0.216899	+	0.375680i
$491$	−11.8275			−0.533769			−0.266885	−	0.963728i	$-0.585994\pi$
$491$	−11.8275			−0.533769			−0.266885	+	0.963728i	$0.585994\pi$
$492$	−6.76484	+	2.01665i	−0.304983	+	0.0909178i
$493$	−2.17859	+	1.25781i	−0.0981190	+	0.0566490i
$494$	6.53406	−	1.66456i	0.293981	−	0.0748921i
$495$	−70.2362	+	3.92620i	−3.15688	+	0.176469i
$496$	2.01263	−	7.51123i	0.0903696	−	0.337264i
$497$	0.815969	+	0.471100i	0.0366012	+	0.0211317i
$498$	−55.5619	+	34.1816i	−2.48979	+	1.53171i
$499$	−18.2263	+	4.88372i	−0.815920	+	0.218625i	−0.642562	−	0.766234i	$-0.722128\pi$
$499$	−18.2263	+	4.88372i	−0.815920	+	0.218625i	−0.173358	+	0.984859i	$0.555462\pi$
$500$	−95.2721	−	25.5281i	−4.26070	−	1.14165i
$501$	−2.69350	+	11.3059i	−0.120337	+	0.505111i
$502$	27.2772	+	7.30891i	1.21744	+	0.326213i
$503$	−20.7493	−	11.9796i	−0.925167	−	0.534146i	−0.0398874	−	0.999204i	$-0.512700\pi$
$503$	−20.7493	−	11.9796i	−0.925167	−	0.534146i	−0.885280	+	0.465059i	$0.846033\pi$
$504$	−4.51385	+	8.93571i	−0.201063	+	0.398028i
$505$	44.2510	+	11.8570i	1.96914	+	0.527630i
$506$	8.45607	+	14.6463i	0.375918	+	0.651109i
$507$	−0.0723497	−	22.5165i	−0.00321316	−	0.999995i
$508$	6.05330	−	10.4846i	0.268572	−	0.465180i
$509$	6.21291	−	6.21291i	0.275382	−	0.275382i	−0.555880	−	0.831263i	$-0.687619\pi$
$509$	6.21291	−	6.21291i	0.275382	−	0.275382i	0.831263	+	0.555880i	$0.187619\pi$
$510$	−6.25621	+	3.84881i	−0.277029	+	0.170428i
$511$		−	2.48323i		−	0.109852i
$512$	7.24835	−	7.24835i	0.320335	−	0.320335i
$513$	−3.92294	+	1.41229i	−0.173202	+	0.0623540i
$514$	−2.97795	−	11.1138i	−0.131352	−	0.490211i
$515$	−2.61651	+	9.76496i	−0.115297	+	0.430296i
$516$	29.7122	−	54.9511i	1.30801	−	2.41909i
$517$		−	0.774479i		−	0.0340615i
$518$	17.7958	+	17.7958i	0.781903	+	0.781903i
$519$	3.85275	+	6.26261i	0.169117	+	0.274898i
$520$	34.6177	+	35.4837i	1.51808	+	1.55606i
$521$			19.3301i			0.846866i	0.905928	+	0.423433i	$0.139175\pi$
$521$			19.3301i			0.846866i	−0.905928	+	0.423433i	$0.860825\pi$
$522$	−29.6898	−	26.5462i	−1.29949	−	1.16189i
$523$	−3.99744	−	6.92376i	−0.174796	−	0.302755i	0.765295	−	0.643680i	$-0.222593\pi$
$523$	−3.99744	−	6.92376i	−0.174796	−	0.302755i	−0.940091	+	0.340925i	$0.889260\pi$
$524$	48.8117			2.13235
$525$	−19.8780	+	5.92578i	−0.867546	+	0.258622i
$526$	2.55813	−	9.54708i	0.111540	−	0.416272i
$527$	0.972767	−	3.63041i	0.0423744	−	0.158143i
$528$	−8.63167	+	2.57317i	−0.375645	+	0.111983i
$529$	−21.3743			−0.929317
$530$	4.51541	+	7.82092i	0.196137	+	0.339719i
$531$	−14.7648	−	13.2015i	−0.640738	−	0.572896i
$532$			2.75370i			0.119388i
$533$	2.09496	+	3.73436i	0.0907427	+	0.161753i
$534$	27.3445	+	44.4483i	1.18331	+	1.92347i
$535$	−34.6716	−	34.6716i	−1.49898	−	1.49898i
$536$		−	16.9694i		−	0.732968i
$537$	−6.95947	+	12.8711i	−0.300323	+	0.555431i
$538$	4.54017	−	16.9442i	0.195741	−	0.730515i
$539$	1.47299	+	5.49728i	0.0634463	+	0.236785i
$540$	−56.1166	−	47.4235i	−2.41488	−	2.04078i
$541$	15.1679	−	15.1679i	0.652120	−	0.652120i	−0.301383	−	0.953503i	$-0.597448\pi$
$541$	15.1679	−	15.1679i	0.652120	−	0.652120i	0.953503	+	0.301383i	$0.0974483\pi$
$542$			26.5178i			1.13904i
$543$	17.0825	−	10.5091i	0.733079	−	0.450989i
$544$	1.41917	−	1.41917i	0.0608463	−	0.0608463i
$545$	6.07814	−	10.5276i	0.260359	−	0.450955i
$546$	14.1157	+	3.54775i	0.604098	+	0.151830i
$547$	18.5739	+	32.1710i	0.794164	+	1.37553i	0.923369	+	0.383915i	$0.125424\pi$
$547$	18.5739	+	32.1710i	0.794164	+	1.37553i	−0.129204	+	0.991618i	$0.541242\pi$
$548$	50.0530	+	13.4117i	2.13816	+	0.572918i
$549$	1.67634	−	3.31852i	0.0715444	−	0.141631i
$550$	−137.565	−	79.4229i	−5.86577	−	3.38660i
$551$	−4.41488	−	1.18296i	−0.188080	−	0.0503960i
$552$	−1.70791	+	7.16893i	−0.0726936	+	0.305130i
$553$	−0.743221	−	0.199145i	−0.0316050	−	0.00846852i
$554$	22.6891	−	6.07954i	0.963969	−	0.258295i
$555$	−65.6350	+	40.3785i	−2.78605	+	1.71397i
$556$	64.2815	+	37.1129i	2.72614	+	1.57394i
$557$	4.33615	−	16.1827i	0.183729	−	0.685685i	−0.811170	−	0.584810i	$-0.801169\pi$
$557$	4.33615	−	16.1827i	0.183729	−	0.685685i	0.994899	−	0.100875i	$-0.0321642\pi$
$558$	59.4108	−	3.32106i	2.51506	−	0.140592i
$559$	−36.4775	−	10.2587i	−1.54284	−	0.433899i
$560$	−3.26033	+	1.88235i	−0.137774	+	0.0795439i
$561$	−4.17196	+	1.24370i	−0.176140	+	0.0525089i
$562$	−29.5870			−1.24805
$563$	−2.29911	−	3.98217i	−0.0968958	−	0.167829i	0.813502	−	0.581562i	$-0.197558\pi$
$563$	−2.29911	−	3.98217i	−0.0968958	−	0.167829i	−0.910398	+	0.413733i	$0.864225\pi$
$564$	0.555781	−	0.587717i	0.0234026	−	0.0247473i
$565$	−2.18714	−	2.18714i	−0.0920137	−	0.0920137i
$566$	2.17537	−	0.582887i	0.0914374	−	0.0245006i
$567$	−8.89878	−	1.34597i	−0.373714	−	0.0565256i
$568$	−1.57207	+	2.72291i	−0.0659628	+	0.114251i
$569$	5.16598	−	8.94775i	0.216569	−	0.375109i	−0.737188	−	0.675688i	$-0.763847\pi$
$569$	5.16598	−	8.94775i	0.216569	−	0.375109i	0.953757	+	0.300579i	$0.0971799\pi$
$570$	−12.9823	−	3.09288i	−0.543769	−	0.129546i
$571$	15.8686	+	9.16172i	0.664079	+	0.383406i	0.793829	−	0.608141i	$-0.208084\pi$
$571$	15.8686	+	9.16172i	0.664079	+	0.383406i	−0.129751	+	0.991547i	$0.541418\pi$
$572$	34.4542	+	61.4164i	1.44060	+	2.56795i
$573$	15.3591	−	9.44887i	0.641635	−	0.394732i
$574$	−2.67348	+	0.716357i	−0.111589	+	0.0299002i
$575$	−13.2237	+	7.63468i	−0.551464	+	0.318388i
$576$	33.2548	+	16.7986i	1.38562	+	0.699942i
$577$	9.36838	+	9.36838i	0.390011	+	0.390011i	0.874691	−	0.484680i	$-0.161064\pi$
$577$	9.36838	+	9.36838i	0.390011	+	0.390011i	−0.484680	+	0.874691i	$0.661064\pi$
$578$	27.6946	−	27.6946i	1.15194	−	1.15194i
$579$	11.1156	+	2.64817i	0.461949	+	0.110054i
$580$	−20.8457	−	77.7971i	−0.865570	−	3.23035i
$581$	−13.9950	+	8.08002i	−0.580611	+	0.335216i
$582$	−58.8976	+	1.64490i	−2.44138	+	0.0681832i
$583$	1.38529	+	5.16999i	0.0573730	+	0.214119i
$584$	8.28660			0.342902
$585$	−20.5842	+	39.5278i	−0.851050	+	1.63427i
$586$	4.62412			0.191021
$587$	5.19551	+	19.3899i	0.214442	+	0.800307i	0.986362	+	0.164588i	$0.0526295\pi$
$587$	5.19551	+	19.3899i	0.214442	+	0.800307i	−0.771921	+	0.635719i	$0.780704\pi$
$588$	−2.82717	+	5.22869i	−0.116591	+	0.215627i
$589$	5.91389	−	3.41438i	0.243677	−	0.140687i
$590$	−16.4081	−	61.2359i	−0.675511	−	2.52104i
$591$	−0.977762	−	3.27989i	−0.0402198	−	0.134917i
$592$	−6.97691	+	6.97691i	−0.286749	+	0.286749i
$593$	−15.0908	−	15.0908i	−0.619705	−	0.619705i	0.325751	−	0.945456i	$-0.394383\pi$
$593$	−15.0908	−	15.0908i	−0.619705	−	0.619705i	−0.945456	+	0.325751i	$0.894383\pi$
$594$	−39.3340	−	56.5959i	−1.61390	−	2.32216i
$595$	−1.57582	+	0.909801i	−0.0646024	+	0.0372982i
$596$	29.4144	−	7.88156i	1.20486	−	0.322841i
$597$	−0.563291	−	20.1693i	−0.0230540	−	0.825476i
$598$	10.7135	+	0.132360i	0.438109	+	0.00541261i
$599$	−12.8357	−	7.41070i	−0.524453	−	0.302793i	0.214302	−	0.976767i	$-0.431252\pi$
$599$	−12.8357	−	7.41070i	−0.524453	−	0.302793i	−0.738755	+	0.673975i	$0.764586\pi$
$600$	−19.7745	−	66.3333i	−0.807291	−	2.70805i
$601$	−22.4155	+	38.8247i	−0.914346	+	1.58369i	−0.106491	+	0.994314i	$0.533961\pi$
$601$	−22.4155	+	38.8247i	−0.914346	+	1.58369i	−0.807856	+	0.589381i	$0.799372\pi$
$602$	12.2469	−	21.2122i	0.499146	−	0.864546i
$603$	14.4924	−	4.76472i	0.590177	−	0.194034i
$604$	−65.1753	+	17.4637i	−2.65195	+	0.710587i
$605$	−62.3168	−	62.3168i	−2.53354	−	2.53354i
$606$	12.8229	+	43.0142i	0.520894	+	1.74733i
$607$	−10.3579	−	17.9404i	−0.420414	−	0.728178i	0.575566	−	0.817755i	$-0.304782\pi$
$607$	−10.3579	−	17.9404i	−0.420414	−	0.728178i	−0.995980	+	0.0895775i	$0.971448\pi$
$608$	3.64652			0.147886
$609$	−7.16839	−	6.77887i	−0.290478	−	0.274694i
$610$	10.3060	−	5.95018i	0.417278	−	0.240916i
$611$	−0.421857	−	0.250558i	−0.0170665	−	0.0101365i
$612$	−4.05841	−	2.05010i	−0.164052	−	0.0828703i
$613$	9.55935	−	35.6760i	0.386099	−	1.44094i	−0.450329	−	0.892863i	$-0.648693\pi$
$613$	9.55935	−	35.6760i	0.386099	−	1.44094i	0.836428	−	0.548077i	$-0.184640\pi$
$614$	−13.5804	−	7.84067i	−0.548062	−	0.316424i
$615$	−0.236596	−	8.47160i	−0.00954047	−	0.341608i
$616$	−18.3446	+	4.91542i	−0.739124	+	0.198048i
$617$	36.8185	+	9.86549i	1.48226	+	0.397170i	0.907115	−	0.420883i	$-0.138280\pi$
$617$	36.8185	+	9.86549i	1.48226	+	0.397170i	0.575143	+	0.818053i	$0.304947\pi$
$618$	−9.49203	+	2.82965i	−0.381825	+	0.113825i
$619$	−10.5337	−	2.82249i	−0.423384	−	0.113446i	0.0408347	−	0.999166i	$-0.486998\pi$
$619$	−10.5337	−	2.82249i	−0.423384	−	0.113446i	−0.464219	+	0.885720i	$0.653665\pi$
$620$	104.212	+	60.1667i	4.18525	+	2.41635i
$621$	−6.60204	+	0.554301i	−0.264931	+	0.0222433i
$622$	−73.8099	−	19.7773i	−2.95951	−	0.792998i
$623$	6.46384	+	11.1957i	0.258968	+	0.448547i
$624$	−1.39091	+	5.53413i	−0.0556808	+	0.221542i
$625$	29.2690	−	50.6953i	1.17076	−	2.02781i
$626$	40.6403	−	40.6403i	1.62431	−	1.62431i
$627$	−6.95770	−	3.76206i	−0.277864	−	0.150242i
$628$		−	6.44176i		−	0.257054i
$629$	−3.37216	+	3.37216i	−0.134457	+	0.134457i
$630$	−21.4752	−	19.2014i	−0.855592	−	0.765001i
$631$	9.25315	+	34.5332i	0.368362	+	1.37475i	0.862806	+	0.505536i	$0.168705\pi$
$631$	9.25315	+	34.5332i	0.368362	+	1.37475i	−0.494444	+	0.869210i	$0.664628\pi$
$632$	0.664554	−	2.48015i	0.0264345	−	0.0986550i
$633$	7.07259	+	11.4964i	0.281110	+	0.456943i
$634$		−	50.3171i		−	1.99835i
$635$	10.2777	+	10.2777i	0.407858	+	0.407858i
$636$	−2.65885	+	4.91738i	−0.105430	+	0.194987i
$637$	3.47090	+	0.976138i	0.137522	+	0.0386760i
$638$		−	75.5543i		−	2.99123i
$639$	−2.76686	−	0.578053i	−0.109455	−	0.0228674i
$640$	40.9028	+	70.8457i	1.61682	+	2.80042i
$641$	−40.4464			−1.59754			−0.798768	−	0.601640i	$-0.794514\pi$
$641$	−40.4464			−1.59754			−0.798768	+	0.601640i	$0.794514\pi$
$642$	11.1335	−	46.7327i	0.439405	−	1.84439i
$643$	3.51112	−	13.1037i	0.138465	−	0.516759i	−0.861495	−	0.507767i	$-0.830471\pi$
$643$	3.51112	−	13.1037i	0.138465	−	0.516759i	0.999960	−	0.00899177i	$-0.00286221\pi$
$644$	−1.13251	+	4.22658i	−0.0446271	+	0.166551i
$645$	54.4923	+	51.5313i	2.14563	+	2.02904i
$646$	−0.825902			−0.0324947
$647$	20.7717	+	35.9776i	0.816619	+	1.41443i	0.908160	+	0.418624i	$0.137488\pi$
$647$	20.7717	+	35.9776i	0.816619	+	1.41443i	−0.0915406	+	0.995801i	$0.529179\pi$
$648$	4.49155	−	29.6955i	0.176445	−	1.16655i
$649$		−	37.5734i		−	1.47489i
$650$	−87.7662	+	49.2364i	−3.44248	+	1.93121i
$651$	14.7347	−	0.411512i	0.577498	−	0.0161284i
$652$	37.4402	+	37.4402i	1.46627	+	1.46627i
$653$			30.4012i			1.18969i	0.803840	+	0.594845i	$0.202787\pi$
$653$			30.4012i			1.18969i	−0.803840	+	0.594845i	$0.797213\pi$
$654$	11.9056	−	0.332501i	0.465546	−	0.0130018i
$655$	−15.1673	+	56.6053i	−0.592637	+	2.21175i
$656$	−0.280850	−	1.04815i	−0.0109654	−	0.0409233i
$657$	2.32673	+	7.07701i	0.0907745	+	0.276100i
$658$	0.224266	−	0.224266i	0.00874278	−	0.00874278i
$659$			20.1964i			0.786740i	0.919380	+	0.393370i	$0.128691\pi$
$659$			20.1964i			0.786740i	−0.919380	+	0.393370i	$0.871309\pi$
$660$	−3.89112	−	139.326i	−0.151462	−	5.42326i
$661$	−15.7685	+	15.7685i	−0.613324	+	0.613324i	−0.943811	−	0.330487i	$-0.892787\pi$
$661$	−15.7685	+	15.7685i	−0.613324	+	0.613324i	0.330487	+	0.943811i	$0.392787\pi$
$662$	−23.5719	+	40.8277i	−0.916147	+	1.58681i
$663$	−0.672269	+	2.67482i	−0.0261088	+	0.103881i
$664$	−26.9633	−	46.7017i	−1.04638	−	1.81238i
$665$	−3.19337	−	0.855662i	−0.123834	−	0.0331812i
$666$	−67.3910	−	34.0424i	−2.61135	−	1.31912i
$667$	−6.28977	−	3.63140i	−0.243541	−	0.140608i
$668$	−22.2434	−	5.96010i	−0.860622	−	0.230603i
$669$	−9.56724	−	9.04736i	−0.369891	−	0.349791i
$670$	47.1668	+	12.6383i	1.82221	+	0.488261i
$671$	6.81275	−	1.82547i	0.263003	−	0.0704715i
$672$	6.92395	+	3.74381i	0.267097	+	0.144421i
$673$	−16.5017	−	9.52725i	−0.636093	−	0.367249i	0.147015	−	0.989134i	$-0.453033\pi$
$673$	−16.5017	−	9.52725i	−0.636093	−	0.367249i	−0.783108	+	0.621886i	$0.786367\pi$
$674$	9.70329	−	36.2132i	0.373757	−	1.39488i
$675$	51.0984	−	35.5133i	1.96678	−	1.36691i
$676$	44.6000	+	1.10219i	1.71538	+	0.0423918i
$677$	25.2436	−	14.5744i	0.970190	−	0.560140i	0.0708959	−	0.997484i	$-0.477414\pi$
$677$	25.2436	−	14.5744i	0.970190	−	0.560140i	0.899294	+	0.437344i	$0.144081\pi$
$678$	0.702321	−	2.94798i	0.0269725	−	0.113216i
$679$	−14.5960			−0.560143
$680$	−3.03603	−	5.25856i	−0.116426	−	0.201657i
$681$	−8.14944	−	1.94151i	−0.312287	−	0.0743987i
$682$	79.8199	+	79.8199i	3.05646	+	3.05646i
$683$	35.1281	−	9.41255i	1.34414	−	0.360161i	0.486171	−	0.873863i	$-0.338393\pi$
$683$	35.1281	−	9.41255i	1.34414	−	0.360161i	0.857968	+	0.513702i	$0.171726\pi$
$684$	−2.58016	−	7.84784i	−0.0986550	−	0.300070i
$685$	−31.1061	+	53.8773i	−1.18850	+	2.05855i
$686$	−1.16531	+	2.01838i	−0.0444919	+	0.0770621i
$687$	−22.2199	+	23.4967i	−0.847743	+	0.896456i
$688$	8.31633	+	4.80143i	0.317057	+	0.183053i
$689$	3.26425	+	0.918021i	0.124358	+	0.0349738i
$690$	−18.6542	−	10.0864i	−0.710153	−	0.383982i
$691$	22.4341	−	6.01119i	0.853432	−	0.228676i	0.194522	−	0.980898i	$-0.437685\pi$
$691$	22.4341	−	6.01119i	0.853432	−	0.228676i	0.658910	+	0.752222i	$0.271018\pi$
$692$	−12.6168	+	7.28429i	−0.479618	+	0.276907i
$693$	−9.34876	−	14.2867i	−0.355130	−	0.542706i
$694$	36.2955	+	36.2955i	1.37776	+	1.37776i
$695$	−63.0129	+	63.0129i	−2.39022	+	2.39022i
$696$	22.6213	−	23.9211i	0.857457	−	0.906728i
$697$	−0.135744	−	0.506603i	−0.00514166	−	0.0191890i
$698$	1.63136	−	0.941867i	0.0617479	−	0.0356502i
$699$	−2.86323	−	4.65416i	−0.108297	−	0.176037i
$700$	−10.6370	−	39.6978i	−0.402041	−	1.50044i
$701$	−39.0783			−1.47597			−0.737984	−	0.674819i	$-0.764222\pi$
$701$	−39.0783			−1.47597			−0.737984	+	0.674819i	$0.764222\pi$
$702$	−43.5530	+	3.11536i	−1.64380	+	0.117582i
$703$	−8.66469			−0.326795
$704$	18.2931	+	68.2706i	0.689445	+	2.57304i
$705$	0.508857	+	0.827143i	0.0191646	+	0.0311520i
$706$	−26.1620	+	15.1047i	−0.984622	+	0.568472i
$707$	2.87781	+	10.7401i	0.108231	+	0.403925i
$708$	26.9634	−	28.5128i	1.01335	−	1.07158i
$709$	−23.1877	+	23.1877i	−0.870831	+	0.870831i	−0.992563	−	0.121732i	$-0.961155\pi$
$709$	−23.1877	+	23.1877i	−0.870831	+	0.870831i	0.121732	+	0.992563i	$0.461155\pi$
$710$	−6.39755	−	6.39755i	−0.240096	−	0.240096i
$711$	2.30472	−	0.128833i	0.0864337	−	0.00483163i
$712$	−37.3604	+	21.5700i	−1.40014	+	0.808371i
$713$	10.4813	−	2.80845i	0.392527	−	0.105177i
$714$	−1.56821	−	0.847937i	−0.0586888	−	0.0317333i
$715$	−81.9285	+	20.8714i	−3.06395	+	0.780546i
$716$	−25.1075	−	14.4958i	−0.938310	−	0.541734i
$717$	−0.786572	+	0.831769i	−0.0293751	+	0.0310630i
$718$	−42.0121	+	72.7670i	−1.56788	+	2.71564i
$719$	8.82883	−	15.2920i	0.329260	−	0.570295i	−0.653105	−	0.757267i	$-0.726534\pi$
$719$	8.82883	−	15.2920i	0.329260	−	0.570295i	0.982365	+	0.186972i	$0.0598675\pi$
$720$	7.52797	−	8.41943i	0.280551	−	0.313773i
$721$	−2.37005	+	0.635053i	−0.0882652	+	0.0236506i
$722$	30.2510	+	30.2510i	1.12582	+	1.12582i
$723$	3.98755	+	0.949987i	0.148299	+	0.0353304i
$724$	19.8693	+	34.4146i	0.738437	+	1.27901i
$725$	68.2153			2.53345
$726$	20.0108	−	83.9948i	0.742670	−	3.11734i
$727$	18.3177	−	10.5757i	0.679366	−	0.392232i	−0.120250	−	0.992744i	$-0.538370\pi$
$727$	18.3177	−	10.5757i	0.679366	−	0.392232i	0.799616	+	0.600511i	$0.205036\pi$
$728$	−3.25740	+	11.5825i	−0.120727	+	0.429276i
$729$	26.6220	−	4.50205i	0.986000	−	0.166743i
$730$	−6.17161	+	23.0328i	−0.228422	+	0.852481i
$731$	4.01955	+	2.32069i	0.148668	+	0.0858337i
$732$	6.47989	+	3.50370i	0.239503	+	0.129500i
$733$	21.6285	−	5.79534i	0.798868	−	0.214056i	0.163781	−	0.986497i	$-0.447631\pi$
$733$	21.6285	−	5.79534i	0.798868	−	0.214056i	0.635087	+	0.772441i	$0.280964\pi$
$734$	−24.1717	−	6.47679i	−0.892194	−	0.239063i
$735$	−5.18504	−	4.90329i	−0.191253	−	0.180861i
$736$	5.59694	+	1.49970i	0.206306	+	0.0552795i
$737$	25.0635	+	14.4704i	0.923227	+	0.533025i
$738$	6.94801	−	4.54656i	0.255760	−	0.167361i
$739$	6.67464	+	1.78846i	0.245531	+	0.0657897i	0.379485	−	0.925198i	$-0.376101\pi$
$739$	6.67464	+	1.78846i	0.245531	+	0.0657897i	−0.133955	+	0.990987i	$0.542768\pi$
$740$	−76.3427	−	132.229i	−2.80641	−	4.86085i
$741$	−4.30013	+	2.57275i	−0.157969	+	0.0945125i
$742$	−1.09593	+	1.89821i	−0.0402330	+	0.0696855i
$743$	−0.886534	+	0.886534i	−0.0325238	+	0.0325238i	−0.723182	−	0.690658i	$-0.757321\pi$
$743$	−0.886534	+	0.886534i	−0.0325238	+	0.0325238i	0.690658	+	0.723182i	$0.257321\pi$
$744$	1.37323	+	49.1700i	0.0503449	+	1.80266i
$745$			36.5599i			1.33945i
$746$	25.2536	−	25.2536i	0.924599	−	0.924599i
$747$	32.3139	−	36.1405i	1.18230	−	1.32231i
$748$	−2.23248	−	8.33173i	−0.0816276	−	0.304638i
$749$	3.08015	−	11.4953i	0.112546	−	0.420028i
$750$	115.974	−	3.23894i	4.23478	−	0.118270i
$751$			50.2073i			1.83209i	0.401076	+	0.916045i	$0.368636\pi$
$751$			50.2073i			1.83209i	−0.401076	+	0.916045i	$0.631364\pi$
$752$	0.0879241	+	0.0879241i	0.00320626	+	0.00320626i
$753$	−20.9785	+	0.585891i	−0.764501	+	0.0213511i
$754$	−41.1543	−	24.4433i	−1.49875	−	0.890171i
$755$		−	81.0081i		−	2.94819i
$756$	3.15805	−	17.5504i	0.114857	−	0.638301i
$757$	−19.0230	−	32.9489i	−0.691404	−	1.19755i	−0.971378	−	0.237540i	$-0.923659\pi$
$757$	−19.0230	−	32.9489i	−0.691404	−	1.19755i	0.279974	−	0.960008i	$-0.409674\pi$
$758$	−23.3023			−0.846376
$759$	−9.13198	−	8.63576i	−0.331470	−	0.313458i
$760$	2.85537	−	10.6564i	0.103575	−	0.386548i
$761$	−6.35189	+	23.7056i	−0.230256	+	0.859326i	0.749975	+	0.661467i	$0.230066\pi$
$761$	−6.35189	+	23.7056i	−0.230256	+	0.859326i	−0.980230	+	0.197860i	$0.936601\pi$
$762$	−3.30031	+	13.8530i	−0.119558	+	0.501841i
$763$	2.95045			0.106813
$764$	17.8648	+	30.9427i	0.646324	+	1.11947i
$765$	3.63851	−	4.06938i	0.131550	−	0.147129i
$766$			73.8467i			2.66819i
$767$	−20.4662	−	12.1557i	−0.738991	−	0.438917i
$768$	−17.6597	+	32.6606i	−0.637241	+	1.17854i
$769$	−5.84686	−	5.84686i	−0.210843	−	0.210843i	0.593782	−	0.804626i	$-0.297634\pi$
$769$	−5.84686	−	5.84686i	−0.210843	−	0.210843i	−0.804626	+	0.593782i	$0.797634\pi$
$770$		−	54.6500i		−	1.96945i
$771$	4.48049	+	7.28300i	0.161361	+	0.262291i
$772$	−5.85977	+	21.8690i	−0.210898	+	0.787082i
$773$	9.47819	+	35.3731i	0.340907	+	1.27228i	0.897322	+	0.441377i	$0.145510\pi$
$773$	9.47819	+	35.3731i	0.340907	+	1.27228i	−0.556415	+	0.830905i	$0.687823\pi$
$774$	−15.0273	+	71.9283i	−0.540144	+	2.58541i
$775$	−72.0665	+	72.0665i	−2.58870	+	2.58870i
$776$		−	48.7072i		−	1.74849i
$777$	−16.4524	−	8.89586i	−0.590226	−	0.319137i
$778$	−12.4989	+	12.4989i	−0.448107	+	0.448107i
$779$	0.476457	−	0.825248i	0.0170708	−	0.0295676i
$780$	−77.1496	−	42.9552i	−2.76240	−	1.53804i
$781$	−2.68113	−	4.64385i	−0.0959383	−	0.166170i
$782$	−1.26766	−	0.339667i	−0.0453313	−	0.0121465i
$783$	26.7810	+	12.6026i	0.957076	+	0.450381i
$784$	−0.791313	−	0.456865i	−0.0282612	−	0.0163166i
$785$	7.47029	+	2.00166i	0.266626	+	0.0714422i
$786$	−55.0232	+	16.4029i	−1.96261	+	0.585070i
$787$	−48.9490	−	13.1158i	−1.74484	−	0.467529i	−0.761330	−	0.648365i	$-0.775453\pi$
$787$	−48.9490	−	13.1158i	−1.74484	−	0.467529i	−0.983513	+	0.180836i	$0.942120\pi$
$788$	6.55019	−	1.75512i	0.233341	−	0.0625235i
$789$	0.205063	+	7.34252i	0.00730043	+	0.261401i
$790$	6.39868	+	3.69428i	0.227655	+	0.131437i
$791$	0.194301	−	0.725141i	0.00690855	−	0.0257830i
$792$	47.6750	−	31.1971i	1.69406	−	1.10854i
$793$	1.20972	−	4.30147i	0.0429585	−	0.152750i
$794$	47.5989	−	27.4813i	1.68922	−	0.975274i
$795$	−4.87634	−	4.61136i	−0.172946	−	0.163548i
$796$	39.9783			1.41699
$797$	16.7799	+	29.0636i	0.594373	+	1.02948i	0.993635	+	0.112648i	$0.0359332\pi$
$797$	16.7799	+	29.0636i	0.594373	+	1.02948i	−0.399262	+	0.916837i	$0.630733\pi$
$798$	−0.925363	−	3.10412i	−0.0327575	−	0.109885i
$799$	0.0424965	+	0.0424965i	0.00150342	+	0.00150342i
$800$	−52.5688	+	14.0858i	−1.85859	+	0.498007i
$801$	−28.9116	−	25.8504i	−1.02154	−	0.913380i
$802$	22.3677	−	38.7421i	0.789832	−	1.36803i
$803$	−7.06628	+	12.2392i	−0.249364	+	0.431910i
$804$	8.63531	+	28.9671i	0.304544	+	1.02159i
$805$	−4.54952	−	2.62667i	−0.160349	−	0.0925778i
$806$	69.3010	−	17.6545i	2.44102	−	0.621854i
$807$	0.363946	+	13.0315i	0.0128115	+	0.458731i
$808$	−35.8401	+	9.60334i	−1.26085	+	0.337844i
$809$	34.7484	−	20.0620i	1.22169	−	0.705343i	0.256412	−	0.966568i	$-0.417460\pi$
$809$	34.7484	−	20.0620i	1.22169	−	0.705343i	0.965278	+	0.261224i	$0.0841262\pi$
$810$	79.1940	+	34.6007i	2.78259	+	1.21574i
$811$	29.7864	+	29.7864i	1.04594	+	1.04594i	0.998893	+	0.0470479i	$0.0149813\pi$
$811$	29.7864	+	29.7864i	1.04594	+	1.04594i	0.0470479	+	0.998893i	$0.485019\pi$
$812$	13.8227	−	13.8227i	0.485080	−	0.485080i
$813$	−5.63005	−	18.8859i	−0.197455	−	0.662359i
$814$	−37.0709	−	138.350i	−1.29933	−	4.84918i
$815$	−55.0521	+	31.7843i	−1.92839	+	1.11336i
$816$	0.332437	−	0.614822i	0.0116376	−	0.0215231i
$817$	2.18259	+	8.14554i	0.0763592	+	0.284976i
$818$	18.5595			0.648916
$819$	−10.8064	+	0.470245i	−0.377607	+	0.0164317i
$820$	16.7918			0.586396
$821$	3.32676	+	12.4156i	0.116105	+	0.433309i	0.999367	−	0.0355702i	$-0.0113247\pi$
$821$	3.32676	+	12.4156i	0.116105	+	0.433309i	−0.883262	+	0.468879i	$0.844658\pi$
$822$	−60.9293	+	1.70164i	−2.12515	+	0.0593516i
$823$	−23.8313	+	13.7590i	−0.830708	+	0.479609i	−0.854095	−	0.520117i	$-0.825888\pi$
$823$	−23.8313	+	13.7590i	−0.830708	+	0.479609i	0.0233873	+	0.999726i	$0.492555\pi$
$824$	−2.11919	−	7.90892i	−0.0738254	−	0.275520i
$825$	114.836	+	27.3582i	3.99806	+	0.952491i
$826$	10.8801	−	10.8801i	0.378568	−	0.378568i
$827$	12.5447	+	12.5447i	0.436220	+	0.436220i	0.890738	−	0.454517i	$-0.150188\pi$
$827$	12.5447	+	12.5447i	0.436220	+	0.436220i	−0.454517	+	0.890738i	$0.650188\pi$
$828$	−0.732656	−	13.1066i	−0.0254616	−	0.455485i
$829$	24.0566	−	13.8891i	0.835520	−	0.482388i	−0.0202186	−	0.999796i	$-0.506436\pi$
$829$	24.0566	−	13.8891i	0.835520	−	0.482388i	0.855739	+	0.517408i	$0.173103\pi$
$830$	149.890	−	40.1629i	5.20275	−	1.39407i
$831$	−14.8684	+	9.14700i	−0.515779	+	0.317306i
$832$	43.1050	+	12.1226i	1.49440	+	0.420276i
$833$	−0.382467	−	0.220817i	−0.0132517	−	0.00765087i
$834$	−84.9331	−	20.2343i	−2.94099	−	0.700657i
$835$	13.8234	−	23.9429i	0.478380	−	0.828579i
$836$	7.83594	−	13.5723i	0.271012	−	0.469406i
$837$	−41.6071	+	14.9789i	−1.43815	+	0.517746i
$838$	59.5677	−	15.9611i	2.05773	−	0.551368i
$839$	0.0867124	+	0.0867124i	0.00299364	+	0.00299364i	0.708602	−	0.705608i	$-0.249326\pi$
$839$	0.0867124	+	0.0867124i	0.00299364	+	0.00299364i	−0.705608	+	0.708602i	$0.749326\pi$
$840$	16.3624	−	17.3026i	0.564557	−	0.596997i
$841$	1.72315	+	2.98459i	0.0594191	+	0.102917i
$842$	32.6234			1.12428
$843$	21.0718	−	6.28168i	0.725752	−	0.216353i
$844$	−23.1609	+	13.3720i	−0.797232	+	0.460282i
$845$	−15.1368	+	51.3786i	−0.520722	+	1.76748i
$846$	−0.429008	+	0.849272i	−0.0147496	+	0.0291986i
$847$	5.53609	−	20.6610i	0.190222	−	0.709920i
$848$	−0.744200	−	0.429664i	−0.0255559	−	0.0147547i
$849$	−1.42554	+	0.876987i	−0.0489243	+	0.0300981i
$850$	11.9063	−	3.19030i	0.408384	−	0.109426i
$851$	−13.2992	−	3.56351i	−0.455891	−	0.122156i
$852$	1.29793	−	5.44804i	0.0444664	−	0.186647i
$853$	35.2512	+	9.44554i	1.20698	+	0.323409i	0.805576	−	0.592492i	$-0.201856\pi$
$853$	35.2512	+	9.44554i	1.20698	+	0.323409i	0.401403	+	0.915901i	$0.368523\pi$
$854$	2.50137	+	1.44417i	0.0855951	+	0.0494183i
$855$	9.90261	−	0.553555i	0.338662	−	0.0189312i
$856$	38.3600	+	10.2785i	1.31112	+	0.351313i
$857$	−5.37910	−	9.31687i	−0.183747	−	0.318258i	0.759407	−	0.650616i	$-0.225489\pi$
$857$	−5.37910	−	9.31687i	−0.183747	−	0.318258i	−0.943153	+	0.332358i	$0.892156\pi$
$858$	−59.4772	−	57.6537i	−2.03052	−	1.96826i
$859$	−16.7897	+	29.0806i	−0.572857	+	0.992218i	0.423414	+	0.905936i	$0.360832\pi$
$859$	−16.7897	+	29.0806i	−0.572857	+	0.992218i	−0.996271	+	0.0862813i	$0.972502\pi$
$860$	−105.076	+	105.076i	−3.58308	+	3.58308i
$861$	1.75196	−	1.07780i	0.0597065	−	0.0367313i
$862$			26.7346i			0.910583i
$863$	1.79154	−	1.79154i	0.0609846	−	0.0609846i	−0.675957	−	0.736941i	$-0.736269\pi$
$863$	1.79154	−	1.79154i	0.0609846	−	0.0609846i	0.736941	+	0.675957i	$0.236269\pi$
$864$	−23.2406	−	4.18196i	−0.790662	−	0.142273i
$865$	−4.52692	−	16.8947i	−0.153920	−	0.574437i
$866$	2.10197	−	7.84465i	0.0714277	−	0.266572i
$867$	−13.8441	+	25.6039i	−0.470171	+	0.869554i
$868$			29.2061i			0.991319i
$869$	3.09645	+	3.09645i	0.105040	+	0.105040i
$870$	49.6416	+	80.6920i	1.68301	+	2.73572i
$871$	15.9905	−	8.97060i	0.541819	−	0.303957i
$872$			9.84572i			0.333418i
$873$	41.5975	−	13.6761i	1.40786	−	0.462867i
$874$	−1.19222	−	2.06499i	−0.0403275	−	0.0698493i
$875$	28.7407			0.971614
$876$	−14.1453	+	4.21684i	−0.477927	+	0.142474i
$877$	12.3486	−	46.0854i	0.416981	−	1.55619i	−0.363854	−	0.931456i	$-0.618539\pi$
$877$	12.3486	−	46.0854i	0.416981	−	1.55619i	0.780835	−	0.624738i	$-0.214794\pi$
$878$	14.8524	−	55.4301i	0.501245	−	1.87067i
$879$	−3.29328	+	0.981755i	−0.111080	+	0.0331138i
$880$	21.4257			0.722261
$881$	−18.2887	−	31.6770i	−0.616163	−	1.06723i	−0.990179	−	0.139804i	$-0.955353\pi$
$881$	−18.2887	−	31.6770i	−0.616163	−	1.06723i	0.374016	−	0.927422i	$-0.377981\pi$
$882$	1.42987	−	6.84411i	0.0481463	−	0.230453i
$883$		−	35.9469i		−	1.20971i	−0.796336	−	0.604855i	$-0.793231\pi$
$883$		−	35.9469i		−	1.20971i	0.796336	−	0.604855i	$-0.206769\pi$
$884$	−5.26053	−	1.47944i	−0.176931	−	0.0497591i
$885$	24.6869	+	40.1284i	0.829841	+	1.34890i
$886$	−36.0155	−	36.0155i	−1.20996	−	1.20996i
$887$		−	26.3548i		−	0.884909i	−0.896791	−	0.442454i	$-0.854108\pi$
$887$		−	26.3548i		−	0.884909i	0.896791	−	0.442454i	$-0.145892\pi$
$888$	29.6857	−	54.9021i	0.996188	−	1.84239i
$889$	−0.913049	+	3.40755i	−0.0306227	+	0.114285i
$890$	−32.1294	−	119.909i	−1.07698	−	4.01935i
$891$	40.0296	+	31.9563i	1.34104	+	1.07058i
$892$	18.4483	−	18.4483i	0.617695	−	0.617695i
$893$			0.109194i			0.00365403i
$894$	−30.5089	+	18.7690i	−1.02037	+	0.627730i
$895$	24.6120	−	24.6120i	0.822688	−	0.822688i
$896$	−9.92749	+	17.1949i	−0.331654	+	0.574442i
$897$	−7.65825	+	2.18034i	−0.255702	+	0.0727996i
$898$	−21.4143	−	37.0906i	−0.714604	−	1.23773i
$899$	−46.8248	−	12.5467i	−1.56169	−	0.418455i
$900$	67.5107	+	103.169i	2.25036	+	3.43897i
$901$	−0.359696	−	0.207670i	−0.0119832	−	0.00691850i
$902$	15.2153	+	4.07694i	0.506615	+	0.135747i
$903$	−4.21859	+	17.7075i	−0.140386	+	0.589267i
$904$	2.41982	+	0.648388i	0.0804819	+	0.0215651i
$905$	−46.0835	+	12.3480i	−1.53187	+	0.410463i
$906$	67.6005	−	41.5877i	2.24588	−	1.38166i
$907$	19.0769	+	11.0140i	0.633438	+	0.365715i	0.782082	−	0.623175i	$-0.214158\pi$
$907$	19.0769	+	11.0140i	0.633438	+	0.365715i	−0.148644	+	0.988891i	$0.547491\pi$
$908$	4.29610	−	16.0333i	0.142571	−	0.532083i
$909$	−18.2648	−	27.9121i	−0.605806	−	0.925787i
$910$	−29.7678	−	17.6803i	−0.986791	−	0.586096i
$911$	−20.4917	+	11.8309i	−0.678921	+	0.391975i	−0.799449	−	0.600735i	$-0.794875\pi$
$911$	−20.4917	+	11.8309i	−0.678921	+	0.391975i	0.120527	+	0.992710i	$0.461542\pi$
$912$	1.21698	−	0.362792i	0.0402983	−	0.0120132i
$913$	91.9701			3.04377
$914$	−5.44845	−	9.43699i	−0.180219	−	0.312148i
$915$	−6.07662	+	6.42579i	−0.200887	+	0.212430i
$916$	−45.3082	−	45.3082i	−1.49703	−	1.49703i
$917$	−13.7386	+	3.68126i	−0.453690	+	0.121566i
$918$	5.26378	+	0.947176i	0.173731	+	0.0312615i
$919$	18.5891	−	32.1973i	0.613198	−	1.06209i	−0.377500	−	0.926010i	$-0.623216\pi$
$919$	18.5891	−	32.1973i	0.613198	−	1.06209i	0.990698	−	0.136080i	$-0.0434505\pi$
$920$	8.76526	−	15.1819i	0.288982	−	0.500531i
$921$	11.3366	+	2.70082i	0.373554	+	0.0889949i
$922$	9.43753	+	5.44876i	0.310808	+	0.179445i
$923$	−3.39689	−	0.0419668i	−0.111810	−	0.00138136i
$924$	28.8131	−	17.7258i	0.947882	−	0.583135i
$925$	124.912	−	33.4700i	4.10707	−	1.10049i
$926$	−33.0743	+	19.0954i	−1.08689	+	0.627515i
$927$	6.15943	−	4.03054i	0.202302	−	0.132380i
$928$	−18.3043	−	18.3043i	−0.600868	−	0.600868i
$929$	−30.8527	+	30.8527i	−1.01224	+	1.01224i	−0.0123189	+	0.999924i	$0.503921\pi$
$929$	−30.8527	+	30.8527i	−1.01224	+	1.01224i	−0.999924	+	0.0123189i	$0.996079\pi$
$930$	−137.692	−	32.8034i	−4.51509	−	1.07567i
$931$	−0.207677	−	0.775062i	−0.00680635	−	0.0254016i
$932$	9.37635	−	5.41344i	0.307133	−	0.177323i
$933$	56.7662	−	1.58537i	1.85844	−	0.0519028i
$934$	−12.2768	−	45.8175i	−0.401708	−	1.49919i
$935$	10.3557			0.338668
$936$	−1.56922	−	36.0613i	−0.0512916	−	1.17870i
$937$	−30.3914			−0.992844			−0.496422	−	0.868081i	$-0.665353\pi$
$937$	−30.3914			−0.992844			−0.496422	+	0.868081i	$0.665353\pi$
$938$	3.06744	+	11.4478i	0.100155	+	0.373785i
$939$	−20.3155	+	37.5723i	−0.662971	+	1.22613i
$940$	−1.66638	+	0.962082i	−0.0543512	+	0.0313797i
$941$	9.21723	+	34.3992i	0.300473	+	1.12138i	0.936773	+	0.349939i	$0.113798\pi$
$941$	9.21723	+	34.3992i	0.300473	+	1.12138i	−0.636300	+	0.771442i	$0.719536\pi$
$942$	2.16471	+	7.26149i	0.0705301	+	0.236592i
$943$	1.07070	−	1.07070i	0.0348668	−	0.0348668i
$944$	4.26559	+	4.26559i	0.138833	+	0.138833i
$945$	19.3713	+	9.11574i	0.630147	+	0.296535i
$946$	−120.723	+	69.6996i	−3.92505	+	2.26613i
$947$	−1.88689	+	0.505591i	−0.0613157	+	0.0164295i	−0.289347	−	0.957224i	$-0.593438\pi$
$947$	−1.88689	+	0.505591i	−0.0613157	+	0.0164295i	0.228031	+	0.973654i	$0.426771\pi$
$948$	0.127682	+	4.57182i	0.00414693	+	0.148486i
$949$	4.38057	+	7.80859i	0.142199	+	0.253477i
$950$	19.3952	+	11.1978i	0.629265	+	0.363306i
$951$	10.6829	+	35.8357i	0.346417	+	1.16205i
$952$	0.736873	−	1.27630i	0.0238822	−	0.0413652i
$953$	13.1563	−	22.7874i	0.426174	−	0.738155i	−0.570355	−	0.821398i	$-0.693194\pi$
$953$	13.1563	−	22.7874i	0.426174	−	0.738155i	0.996529	+	0.0832429i	$0.0265277\pi$
$954$	1.34474	−	6.43662i	0.0435376	−	0.208393i
$955$	−41.4343	+	11.1023i	−1.34078	+	0.359261i
$956$	−1.60388	−	1.60388i	−0.0518733	−	0.0518733i
$957$	16.0411	+	53.8096i	0.518535	+	1.73942i
$958$	33.2079	+	57.5178i	1.07290	+	1.85832i
$959$	−15.0995			−0.487588
$960$	−64.3929	−	60.8939i	−2.07827	−	1.96534i
$961$	35.8766	−	20.7133i	1.15731	−	0.668173i
$962$	−87.3524	−	24.5665i	−2.81635	−	0.792056i
$963$	1.99265	+	35.6467i	0.0642121	+	1.14870i
$964$	−2.10210	+	7.84514i	−0.0677041	+	0.252675i
$965$	−23.5399	−	13.5908i	−0.757776	−	0.437502i
$966$	−0.143690	−	5.14500i	−0.00462316	−	0.165538i
$967$	−10.8644	+	2.91110i	−0.349374	+	0.0936145i	−0.429238	−	0.903191i	$-0.641218\pi$
$967$	−10.8644	+	2.91110i	−0.349374	+	0.0936145i	0.0798642	+	0.996806i	$0.474551\pi$
$968$	68.9463	+	18.4741i	2.21602	+	0.593780i
$969$	0.588205	−	0.175349i	0.0188959	−	0.00563302i
$970$	135.383	+	36.2757i	4.34687	+	1.16474i
$971$	14.9882	+	8.65344i	0.480994	+	0.277702i	0.720831	−	0.693111i	$-0.243760\pi$
$971$	14.9882	+	8.65344i	0.480994	+	0.277702i	−0.239836	+	0.970813i	$0.577094\pi$
$972$	7.44414	+	52.9763i	0.238771	+	1.69921i
$973$	−20.8918	−	5.59793i	−0.669759	−	0.179461i
$974$	−17.0704	−	29.5668i	−0.546970	−	0.947380i
$975$	52.0534	−	53.6998i	1.66704	−	1.71977i
$976$	−0.566190	+	0.980670i	−0.0181233	+	0.0313905i
$977$	−1.07099	+	1.07099i	−0.0342639	+	0.0342639i	−0.724031	−	0.689767i	$-0.757713\pi$
$977$	−1.07099	+	1.07099i	−0.0342639	+	0.0342639i	0.689767	+	0.724031i	$0.257713\pi$
$978$	−54.7862	−	29.6231i	−1.75187	−	0.947242i
$979$		−	73.5741i		−	2.35144i
$980$	9.99821	−	9.99821i	0.319381	−	0.319381i
$981$	−8.40855	+	2.76451i	−0.268464	+	0.0882639i
$982$	7.13450	+	26.6263i	0.227671	+	0.849679i
$983$	−2.15412	+	8.03927i	−0.0687056	+	0.256413i	−0.991732	−	0.128323i	$-0.959041\pi$
$983$	−2.15412	+	8.03927i	−0.0687056	+	0.256413i	0.923027	+	0.384736i	$0.125707\pi$
$984$	3.59665	+	5.84632i	0.114657	+	0.186374i
$985$			8.14141i			0.259407i
$986$	4.14575	+	4.14575i	0.132028	+	0.132028i
$987$	−0.112107	+	0.207336i	−0.00356841	+	0.00659957i
$988$	−4.85771	−	8.65910i	−0.154544	−	0.275483i
$989$			13.4000i			0.426095i
$990$	51.2059	+	155.748i	1.62743	+	4.95001i
$991$	−12.6608	−	21.9292i	−0.402185	−	0.696605i	0.591804	−	0.806082i	$-0.298416\pi$
$991$	−12.6608	−	21.9292i	−0.402185	−	0.696605i	−0.993989	+	0.109477i	$0.965082\pi$
$992$	38.6754			1.22795
$993$	8.11963	−	34.0820i	0.257669	−	1.08156i
$994$	0.568345	−	2.12109i	0.0180268	−	0.0672769i
$995$	−12.4225	+	46.3614i	−0.393820	+	1.46976i
$996$	69.7920	+	65.9996i	2.21144	+	2.09128i
$997$	−20.9366			−0.663070			−0.331535	−	0.943443i	$-0.607567\pi$
$997$	−20.9366			−0.663070			−0.331535	+	0.943443i	$0.607567\pi$
$998$	21.9886	+	38.0853i	0.696035	+	1.20557i
$999$	55.2233	+	9.93699i	1.74719	+	0.314392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fy.a.50.10	yes	336
9.2	odd	6		819.2.ew.a.596.75	✓	336
13.6	odd	12		819.2.ew.a.617.75	yes	336
117.110	even	12	inner	819.2.fy.a.344.10	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.596.75	✓	336	9.2	odd	6
819.2.ew.a.617.75	yes	336	13.6	odd	12
819.2.fy.a.50.10	yes	336	1.1	even	1	trivial
819.2.fy.a.344.10	yes	336	117.110	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fy (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.603210 - 2.25121i) q^{2} +(0.907564 + 1.47524i) q^{3} +(-2.97204 + 1.71591i) q^{4} +(-1.06637 - 3.97976i) q^{5} +(2.77362 - 2.93300i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.35963 + 2.35963i) q^{8} +(-1.35266 + 2.67775i) q^{9} +O(q^{10})\)	\(q+(-0.603210 - 2.25121i) q^{2} +(0.907564 + 1.47524i) q^{3} +(-2.97204 + 1.71591i) q^{4} +(-1.06637 - 3.97976i) q^{5} +(2.77362 - 2.93300i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.35963 + 2.35963i) q^{8} +(-1.35266 + 2.67775i) q^{9} +(-8.31604 + 4.80127i) q^{10} +(-5.49728 + 1.47299i) q^{11} +(-5.22869 - 2.82717i) q^{12} +(-0.976138 + 3.47090i) q^{13} +(-2.01838 - 1.16531i) q^{14} +(4.90329 - 5.18504i) q^{15} +(0.456865 - 0.791313i) q^{16} +(0.220817 - 0.382467i) q^{17} +(6.84411 + 1.42987i) q^{18} +(0.775062 - 0.207677i) q^{19} +(9.99821 + 9.99821i) q^{20} +(1.68490 + 0.401407i) q^{21} +(6.63203 + 11.4870i) q^{22} +1.27503 q^{23} +(-1.33950 + 5.62254i) q^{24} +(-10.3712 + 5.98782i) q^{25} +(8.40255 + 0.103809i) q^{26} +(-5.17793 + 0.434735i) q^{27} +(-0.888219 + 3.31488i) q^{28} +(-4.93302 - 2.84808i) q^{29} +(-14.6303 - 7.91068i) q^{30} +(8.22040 - 2.20265i) q^{31} +(4.38964 + 1.17620i) q^{32} +(-7.16215 - 6.77297i) q^{33} +(-0.994213 - 0.266399i) q^{34} +(-3.56816 - 2.06008i) q^{35} +(-0.574617 - 10.2794i) q^{36} +(-10.4305 - 2.79484i) q^{37} +(-0.935051 - 1.61956i) q^{38} +(-6.00631 + 1.71003i) q^{39} +(6.87453 - 11.9070i) q^{40} +(0.839742 - 0.839742i) q^{41} +(-0.112695 - 4.03519i) q^{42} +10.5095i q^{43} +(13.8106 - 13.8106i) q^{44} +(12.0992 + 2.52777i) q^{45} +(-0.769114 - 2.87037i) q^{46} +(-0.0352210 + 0.131446i) q^{47} +(1.58201 - 0.0441826i) q^{48} -1.00000i q^{49} +(19.7359 + 19.7359i) q^{50} +(0.764635 - 0.0213548i) q^{51} +(-3.05463 - 11.9906i) q^{52} -0.940462i q^{53} +(4.10206 + 11.3944i) q^{54} +(11.7243 + 20.3071i) q^{55} +3.33703 q^{56} +(1.00979 + 0.954921i) q^{57} +(-3.43599 + 12.8233i) q^{58} +(-1.70873 + 6.37705i) q^{59} +(-5.67573 + 23.8238i) q^{60} -1.23929 q^{61} +(-9.91726 - 17.1772i) q^{62} +(0.936980 + 2.84992i) q^{63} -12.4190i q^{64} +(14.8543 + 0.183517i) q^{65} +(-10.9271 + 20.2090i) q^{66} +(-3.59577 - 3.59577i) q^{67} +1.51561i q^{68} +(1.15717 + 1.88098i) q^{69} +(-2.48532 + 9.27533i) q^{70} +(0.243859 + 0.910095i) q^{71} +(-9.51028 + 3.12673i) q^{72} +(1.75591 - 1.75591i) q^{73} +25.1671i q^{74} +(-18.2460 - 9.86568i) q^{75} +(-1.94716 + 1.94716i) q^{76} +(-2.84560 + 4.92873i) q^{77} +(7.47271 + 12.4900i) q^{78} +(-0.384719 - 0.666354i) q^{79} +(-3.63643 - 0.974377i) q^{80} +(-5.34064 - 7.24414i) q^{81} +(-2.39698 - 1.38390i) q^{82} +(-15.6094 - 4.18253i) q^{83} +(-5.69635 + 1.69813i) q^{84} +(-1.75760 - 0.470948i) q^{85} +(23.6592 - 6.33946i) q^{86} +(-0.275433 - 9.86220i) q^{87} +(-16.4473 - 9.49585i) q^{88} +(-3.34593 + 12.4872i) q^{89} +(-1.60783 - 28.7627i) q^{90} +(1.76406 + 3.14453i) q^{91} +(-3.78945 + 2.18784i) q^{92} +(10.7100 + 10.1280i) q^{93} +0.317159 q^{94} +(-1.65301 - 2.86310i) q^{95} +(2.24870 + 7.54325i) q^{96} +(-10.3209 - 10.3209i) q^{97} +(-2.25121 + 0.603210i) q^{98} +(3.49163 - 16.7128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) 336 * q - 12 * q^6 + 36 * q^8	\( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

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